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\vskip 2.5in

\centerline {Membership of Low-Mass Stars in the}
\centerline {Open Cluster $\alpha$ Persei$^1$}
\vskip .7in

\centerline { Charles F. Prosser$^2$}

\vskip .3in

\centerline {University of California Observatories/Lick Observatory,}
\centerline {Board of Studies in Astronomy and Astrophysics,}
\centerline {University of California, Santa Cruz  95064}

\vskip 3.5in
\centerline{published in Astronomical Journal 1992, 103, 488}
\vskip .5in

%\noindent{ send proofs to:}

%\centerline{ Charles F. Prosser}
%\centerline{ Center for Astrophysics}
%\centerline{ 60 Garden St.  ~MS-66}
%\centerline{ Cambridge, MA 02138}

\vfill
\noindent{$^1$UCO/Lick Observatory Bulletin No. 1201}

\noindent{$^2$presently at Center for Astrophysics, Cambridge, MA.}

\eject

\singlespace
%\doublespace
\centerline {Abstract}

     The results of a combined astrometric, photometric, and spectroscopic
search for low-mass members in the intermediate-age open
cluster $\alpha$ Persei are presented.  
Over 130 low-mass new members have been identified to
${\rm M}_{\rm V} \simeq 12.5$, almost doubling the previous number
of known members.  The new membership information suggests a slight
upward revision of $\alpha$ Per's age to $\sim 8 \times 10^7$ yrs.  
$\alpha$ Per is noticeably spatially elongated in a
direction  parallel to the Galactic plane, most likely due to tidal
deformation.  Analysis of the distribution of relative H$\alpha$ emission
strengths among $\alpha$ Per members confirms the view that the
mean H$\alpha$ strength decreases in increasingly older systems.  
Allowing for survey incompleteness, one cannot reject the idea that the
luminosity function is consistent with the field luminosity
function to ${\rm M}_{\rm V} \simeq 9$ or 10.


\vskip.3in
\centerline{1. Introduction}

     van den Bergh \& Sher (1960) 
found from studying several open clusters that in general 
the faint end of the cluster luminosity
function decreased or remained constant down to the level of observation.
If true, the
observed cluster luminosity functions are unable to account for
the luminosity function of nearby field stars which increases to faint
magnitudes.  One possible solution is that additional unidentified
low-mass stars exist in most (or all) open clusters. 

  Recent studies in the Hyades (Weis
\& Hanson 1988,  Griffin {\it et al.} 1988, Stauffer 1982),
Pleiades (Stauffer {\it et al.} 1991, Prosser {\it et al.} 1991),
and Praesepe (Mermilliod {\it et al.} 1990, Jones \& Stauffer
1991) have identified faint candidate members.  It is the aim of this
study to determine the existence, and some of the properties, of the
low-mass membership in the open cluster $\alpha$ Persei.
$\alpha$ Per was chosen for study because of the limited
information on low-mass membership, because it is nearby
(which enables both proper motion analysis and observation of
low-mass candidates), because no other clusters of the same 
relatively youthful age have been studied completely, and because of the
existence of the photographic plate material needed for the
proper motion analysis.  


    After a brief review of the history and previous work in
this cluster, the proper motion survey of this study is described.
This is accompanied by a description of the CCD photometry and
spectrocopy programs employed to aid in identifying cluster members.
A review of current information on previous members and possible
members is also given, followed  by a section presenting the new
members and candidate members found in this study.  An
analysis of some cluster properties including luminosity function,
age, spatial distribution of members, reddening, H$\alpha$ emission
strengths, and rotational velocity distribution is presented.
Finally, the last section provides a general review of the 
results found in $\alpha$ Per.  

\vskip .3in
\centerline{2. History and Previous Work.}

     The $\alpha$ Persei cluster is not a strikingly apparent cluster
visually,  because its low galactic latitude ({\it b} $= -7^{\circ}$)
projects it onto a high stellar density field. 
Boss (1910), Eddington (1910), and Kapteyn (1910)  
showed that a number of early-type stars in the direction of $\alpha$
Per shared a common motion.   They correctly interpreted this common motion
in space as evidence for the existence of a cluster.

     A landmark investigation of the bright membership down
to V $\simeq 12$ was made by Heckmann {\it et al.} (1956) and
Heckmann \& L\"ubeck (1958). 
These studies provide the most complete {\it bright} membership list to 
date.  UBV photometry (Mitchell 1960) of Heckmann's candidates provided
not only reddening and distance estimates but also a means for further analysis
and rejection of non-members.  These studies produced a list of 
$\sim 150$ members and likely members down to V $\simeq 12$ 
(${\rm M}_{\rm V} \sim 6$).  
Further analysis of the cluster's membership 
required radial velocity determinations, and this was provided 
for most stars by Petrie \& Heard (1970) and Kraft (1967a).  
With a high background field star density and low (but measurable)
relative proper motion, the identification of fainter members of $\alpha$
Per was a daunting task until the appearance and
application of automatic scanning measuring machines which enable one to
rapidly scan for magnitudes and positions, as in Stauffer {\it et al.} (1989). 
Altogether, Stauffer {\it et al.} (1985,1989) identified  $\sim$ 80 members over
a limited region down to V$=16.5$ ($\sim 30$ Heckmann {\it et al.} (HE)
stars and $\sim 50$ confirmed new members).

     Due to $\alpha$ Per's low galactic latitude and small relative proper
motion, members must be identified not only on the basis of proper
motion and photometry, but also on radial velocity, spectral type, 
chromospheric H$\alpha$ emission (faint end), and, if possible, the presence
of lithium.  This program therefore has required a variety of methods of 
analysis and measurement: astrometric measurements, CCD photometry,
low-resolution CCD spectroscopy, and high-resolution (echelle) CCD 
spectroscopy.

\vskip .3in
\centerline{3. Proper Motion Survey.}

     Because the purpose of this research is a search for faint
members, the brighter stars 
have been neglected.  The Palomar Schmidt $6^{\circ} \times 6^{\circ}$ field 
[E/O 1249, plate center: 3h 30m 44s, $+48^{\circ} 19' 13''$ (1950)] 
covers most of the $\alpha$ Per cluster.  The entire blue and red Schmidt
plates for this field were scanned for magnitudes and positions
with the Minnesota scanning machine, producing a sample of 
over 330,000 stars. It was from a color-selected sample of a portion
of this scanning output that Stauffer {\it et al.} (1989) obtained their
list of candidates to be measured for proper motion.
The same procedure was adopted here, but now including
stars over the entire Schmidt field. 
We chose the same color selection as Stauffer {\it et al.} (1989). 
Figure 1 shows a fraction of the stars scanned, with 
the color-selection based on previous members indicated.
The new color-selected sample went to 
the plate limit and included approximately 30,000 stars.  
Stars of bad image quality were deleted. 
The Minnesota
scan output provided the following characteristics of the image
quality and shape: (1) goodness of fit of
a circle to the image, (2) the difference in the diameter between
ellipse fitting and circular fitting of the image, and (3) the distance
between the image centers as found on the red and blue plates.  By 
comparing objects of different image quality on the plate, we placed 
a subjective limit on these characteristics -- leaving a sample 
of about 24,500 stars.

     The sample was measured in groups of 1000 stars at a time, 
the maximum number of measurements that can be accommodated
at one time on the Lick Automatic Measuring
Engine (AME).  Each star was measured on four Schmidt plates
(two blue, two red) in both direct and reverse orientations.  The Schmidt
plates used are identified in Table 1.   The direct
and reverse measures were combined and averaged, discarding discrepant
measures.  In the end, a little over 23,000 stars,
or 94\% of the input sample, were successfully measured for proper
motions.  Those which could not be accurately measured 
typically had poor image quality or image blending with other
stars.  Proper motions were determined using a modified
central-plate-overlap iterative technique as described in Jones \&
Walker (1988).
The typical one-sigma error in the proper motions 
was $0\arcsecpoint6$ to $0\arcsecpoint7$~ cent$^{-1}$.  
Figure 2 shows the cluster proper motion vector point diagram for regions
measured near the central part of the cluster.
The center of the cluster's distribution in the proper motion diagram 
is seen to be ($+1.9,-2.4$). 

A box region was defined about the cluster center in the proper motion
diagram, extending $\pm 2.5 \sigma$ (where $\sigma = 0\arcsecpoint6 $~cent
$^{-1}$), containing 1784 stars selected for further study.  
The size of this region could not
be enlarged much without significantly encroaching upon the field star
distribution about (0,0).  When all Schmidt proper motions are plotted,
the cluster condensation does not stand out 
as clearly as it does in Figure 2 where only
regions spatially near the cluster center were considered.
  
     Many of the brighter stars (V$\leq 16.0$) were also measured 
on astrograph plates
taken at Lick Observatory for its Northern Proper Motion (NPM) program.  
Table 2 catalogues
the astrograph plates available for the fields which cover a significant
part of the area of the sky encompassed by the Palomar Schmidt field.  Some
stars were measured on more than one astrograph field due to their location.
Once the astrograph fields were all measured, those stars with small errors
in their proper motions ($< 1\arcsecpoint0 ~{\rm cent}^{-1}$) determined from astrograph 
plates alone were used to transform the astrograph system of proper motions onto
the Schmidt system.  The multiple proper motions were then averaged, with
any largely discrepant determinations being rejected.  As a result of
averaging the Schmidt and astrograph proper motions,
many of the stars
moved out of the original box region, generally towards the field 
distribution at (0,0). 
The astrograph plates, taken in blue and yellow simultaneously, also
provide the additional benefit of fairly accurate magnitudes and
colors ($\pm 0\magpoint2$) for the stars - providing a 
further discriminant in the selection of cluster candidates.  
The B and V magnitudes from the 9062 and 9168 
astrograph fields were used for a further color selection.  Almost half
of the 779 stars measured (339 stars) were rejected as having
photographic photometry incompatible with membership.  

     The averaged proper motions were used
to select likely new candidate members to the cluster.  The `AP' stars,
members identified by Stauffer {\it et al.} (1985,1989), recovered in 
this survey were
used to guide the proper motion selection criteria.  Figure 3 shows
the proper motion diagram for the group with the recovered AP members
indicated.  Stars at a 
radial distance greater than $1\arcsecpoint25~ {\rm cent}^{-1}$ 
from the cluster motion
were rejected as proper motion nonmembers.  The spread
of the known AP members indicated that the 237 stars within 
the $1\arcsecpoint25~ {\rm cent}^{-1}$ radius 
needed further observation to determine their membership
status.  An additional 79 stars within the same proper motion limit, 
but without accurate astrograph magnitudes, were also included as candidates.
Thus, a total of 316 candidates
down to the limiting magnitude of the astrograph plates (V$\simeq 16$)
was obtained from the sequence of color and proper motion selections.
These candidates were later
augmented by another group of almost 400 stars included in
the original 1784, but which were too faint to be measured on astrograph
plates.  Their proper motions were derived from Schmidt
plate measures alone.  They satisfy the same criteria as the
brighter candidates, falling within a radius of $1\arcsecpoint25~ {\rm cent}
^{-1}$
from the cluster motion in the proper motion diagram.  The bright
and faint proper motion candidates combined bring the total number
of candidates to approximately 715. 

     Since not all 715 candidates are actual members, additional membership
criteria must be used.
The photometry used in the color-selection is not of the highest
accuracy and, due to the cluster's low galactic latitude, one can
expect a significant number of field stars along the line of sight to show proper
motions similar to that of the cluster.  Accurate 
photometry is needed to further accurately locate members.  In addition,
in a cluster as young as $\alpha$ Per ($\sim 5 \times 10^7$  yrs)
the low-mass stars will exhibit H$\alpha$ in emission
(Stauffer {\it et al.} 1984, Herbig 1985).  
For the brighter candidates,
which are generally too early in spectral type to show H$\alpha$
emission, radial velocities measured from high resolution echelle 
spectra can be used to confirm membership.  The
echelle spectra can also be used for
the detection of the presence of the $\lambda 6707$\AA ~Li line,
another piece of evidence supporting cluster membership.

A second proper motion survey of the Lick astrograph plate field 9062
was later performed in an attempt to identify low-mass cluster members
beyond the boundaries of the Schmidt plate field.   This preliminary
survey yielded one additional member (AP 119 in Table 10). 

\vskip .3in
\centerline{4. BVI CCD Photometry.}

      Photometry of the candidate members in $\alpha$ Per was obtained
at the 1-m Nickel Telescope of Lick Observatory using
a TI $500 \times 500$ pixel CCD with 15 $\mu$ pixels at a scale of 
$0\arcsecpoint54$/pixel.  Observations in B, V, and I were obtained,
although B-band observations exist only for the brighter
candidates and the Heckmann {\it et al.} (1956) (HE) stars 
(see section 6).  
V and I magnitudes were determined for the large portion
of the faint candidates.

     DAOPHOT (Stetson 1987) was employed to determine
instrumental magnitudes using aperture photometry with annular sky value
subtraction.  Occasionally, point spread function fitting was used to extract
magnitudes in cases of image blending in crowded fields.
Standard stars in BVI (Kron) from Stauffer {\it et al.}
(1985) were used to correct for first order extinction and to transform
instrumental bvi magnitudes onto the BVI (Kron) system.  
The resulting standard deviations in the fits were: 
$\sigma_{\Delta\rm{V}}= 0.058, \sigma_{\Delta\rm{(V-I)}} = 0.047$, and 
$\sigma_{\Delta\rm{(B-V)}} = 0.026$.

     While multiple observations were averaged, 
for stars in common with Stauffer {\it et al.} (1985,1989) the new photometry
was also averaged with theirs to produce more accurate mean magnitudes.
An exception to this was in cases where we only had V and I magnitudes for
a star in common --- in that case we kept their B$-$V value for the star.
Another exception was for the photometry of known variables, in which
case we kept the mean magnitudes of Stauffer {\it et al.}.




\vskip .3in
\centerline{5. Spectroscopy.}

\vskip .3in
\centerline{{\it 5.1 Low-Dispersion.}}

     Low-dispersion CCD spectra centered on H$\alpha$ ($\lambda 6563$\AA)
were obtained for the faint proper motion candidate members whose V,I photometry
indicated that they were likely members.  The CCD
spectra were taken at the 1-m Nickel and 3-m Shane telescopes of Lick
Observatory at a resolution of $\sim 2.6$ \AA/pix, using 
a 600 ln/mm grism with blaze at $6500$\AA.  The spectra were used for: (1) 
determination of spectral type, (2) detection of H$\alpha$ emission, and
(3) measurement of the equivalent width of H$\alpha$ emission. 

     Spectral types were estimated from the spectra using the index 
calibration from the Pleiades (Prosser {\it et al.} 1991), 
based on the relative strengths of TiO bands.  MK
standards from spectral types K3 to M5.5 (Keenan \& McNeil 1976)
were observed and used to transform the index values measured to a spectral
type.  The spectral types, referred to as pseudo-MK (or `pMK') spectral
types, are good to $\pm 0.5$
in spectral type subclass and can also be used to confirm membership. 
Analysis of the spectroscopic information will be presented in section 8.

\vskip .3in
\centerline{{\it 5.2 High-Dispersion (Echelle)}.}

     A large fraction of the bright candidates were observed
using the Hamilton echelle spectrograph (Vogt 1987) with both the 3-m Shane
and Coud\'e Auxilary telescopes.  The benefit of having several wavelength
orders per observation enabled all of the following analyses:  detection of
weak H$\alpha$ emission, detection of Li absorption ($\lambda 6707$\AA),
determination of radial velocity and rotational velocity, and, in some cases,
classification of SB1 or SB2 status.

     Observations were made using a TI 800 $\times$ 800 pixel CCD which
provided an intermittent wavelength coverage from $\sim 4600$\AA~ to
$\sim 7300$\AA~ over $\sim 50$ orders with each order comprising $\sim 40$\AA~
on the chip.  A slit width of 640 microns was used, corresponding to 
$\sim 1.5''$ on the sky and a projected resolution of $\sim 3$ pixels.
The echelle spectra were reduced in a normal manner that included 
flatfielding, dark count subtraction, and inter-order count subtraction.
The presence of H$\alpha$ emission and/or Li absorption was easily
determined in the spectra, which have a dispersion of $\sim 0.056$\AA/pixel
at these line locations.

     The signal-to-noise of the spectra typically ranged from 30 to 60 
(at $\lambda 5180$).  
Two select orders were used for measurement of radial and rotational
velocities.  One order (110) had a wavelength range from 
$\sim 5163$\AA~ to 5197\AA, and included the strong Mgb I lines at
5168, 5173, and 5184\AA.  The other order (102) covered
the range from 5568\AA~ to 5604\AA~ and contained numerous lines of 
FeI, CaI, and NiI.  The strong Mgb lines are useful in radial velocity
determinations from weak S/N spectra because they provide a strong
cross-correlation spectrum allowing confident centroid identification.

     A radial velocity standard was observed on each night, 
with a spectral type (F-G V) similar to the $\alpha$ Per candidates being
observed.  The candidates' spectra were cross-correlated (in pixel space) with the
radial velocity standard.  A polynomial fit applied to the cross-correlation
curve provided the centroid value and the velocity relative to the standard.
The candidates' observed radial velocities were corrected 
to heliocentric radial velocities.  The Mgb line order
was primarily used for the radial velocity determination.  As a check, 
those radial velocities derived from the Mgb order were compared
for some stars with those derived using order 102 and the values were found
to agree to within the error of measurement.  Errors in the determined
radial velocity ranged from 0.4 pixels ($= \pm1.0$km/s) for slow rotators
($v\sin i \leq 10$km/s) to $\sim$ 2 pixels ($\pm 5.$km/s) for higher rotators
($v\sin i \sim 100$km/s).  

     Rotational velocities were measured 
as follows.  A low rotation ($v\sin i < 10$ km/s) field star was 
observed and reduced in the same manner as the $\alpha$ Per stars.  This 
low rotator's spectrum was then artifically broadened in increasing amounts
by convolving its spectrum with the broadening function due to rotation
(Gray 1976).  The artifically-broadened spectrum was cross-correlated
with the original nonrotating spectrum and the FWHM value of the 
cross-correlation peak measured. 
A calibration curve between FWHM and $v\sin i$ was obtained after
repeating this process for a range in $v\sin i$.  The $\alpha$ Per
star could then be cross-correlated with the nonrotator standard, a FWHM
value measured, and a corresponding $v\sin i$ value determined from the 
calibration curve.

     The orders 110 (with the Mgb lines) and 102 were also used for the
rotational velocity measurements. Because the stars  
range from late-F to K dwarfs, a set of low rotating standards were used:
HR 6831 (F8V, $v\sin i < 6$ km/s), HR 996 (G5V, $v\sin i \leq 5.6$ km/s), and
HD 75935 (G8V, $v\sin i \leq 6$ km/s).  Each program star was cross-correlated
with the standard nearest in spectral type. 
The Mgb lines are unsuitable for measuring rotation for low $v\sin i$ values  
because their line widths are very sensitive to temperature changes (Gray 1976).

     As a check on the rotational velocities, we compared (Table 3) our
rotational velocities with those determined by Soderblom {\it et al.} (1989)
and Kraft (1967b).
Reasonable agreement is found for the order 102 values for $v\sin i < 50$ km/s.
For $v\sin i > 50$ km/s,  the order 102 values fall systematically too high, 
reflecting the difficulty of using weak lines which become easily
`washed-out' at these higher rotational velocities and do not provide a
well defined cross-correlation curve.  
The agreement at large $v\sin i$ using order 110 values, though not perfect, is an improvement.
As a result of the above analysis order 102 was used for rotational
measures for the slow
rotators ($v\sin i \leq 50$ km/s) and order 110 for the rapid rotators
($v\sin i > 50$ km/s).  Based on the comparison to the `standard' $v\sin i$
values, the error in the present $v\sin i$ values for the
slow rotators appears less than $\pm 5$ km/s (with a few
exceptions) while the uncertainty at large $v\sin i$ is on
the order of $\pm 5$ to $\pm 8$ km/s.  
During the course of the field star observations, HR 7034 was found
to be a double-lined binary.


     Echelle spectra were also obtained for the `HE' (Heckmann {\it et al.}
1956)  stars not having previous radial or rotational velocity determinations.  
Two observations each (one with the 3-m Shane and one with the 
Coud\'e Auxiliary (CAT) telescope) of
HE 334, HE 660, and HE 841 were also obtained to compare 
the present $v\sin i$ measures with those of Stauffer {\it et al.}.
Reasonable agreement with their earlier $v\sin i$ values is
obtained (Table 3), with the possible exception of HE 841
for which the present values deviate by $\sim 10$ km/s. 

%\vfill\eject

\centerline{6. Previous Candidate Member Information.}

    As mentioned  in section 2, the researches by Heckmann {\it et al.}
(1956,1958) and Stauffer {\it et al.} (1985,1989) form the basis of all
previously known members of the $\alpha$ Per cluster.  In this section
we provide data on all known members; the HE and 
AP stars.  

    Table 4 lists the HE stars, mainly derived from the 
membership list of Heckmann {\it et al.} (1956). 
In Table 4, the first column lists the HE star number
(followed by `N' if it is a nonmember), followed by the V,B$-$V photometry
from Mitchell (1960), BD identification, and coordinates determined
from the x,y coordinates in arcsec given by 
Heckmann {\it et al.} (1956). The remaining columns give radial and rotational
velocities from a variety of sources, along with membership determinations 
based on photometry (PH), echelle spectra (ECH), presence of Li, a final
membership determination, and some additional notes.  The `Ref' column
contains the reference numbers for the sources (given at the end
of the table) of the radial and/or rotational velocity data.  
Identification of nonmembers in Table 4 was usually based on the star's
photometry and radial velocity.  The mean heliocentric radial velocity
of $\alpha$ Per members is $\sim -2$ km/s.  
Slow rotators ($v\sin i \le 20$ km/s) with radial velocities within
$\sim$ 2 km/s of the cluster mean were considered members; with 
the allowed deviation increasing to several km/s for the most rapidly rotating
stars.  The expected one co-ordinate velocity dispersion is $\sim 0.5$ km/s.
The observed deviations that were
deemed within acceptable membership limits are therefore more than twice 
the theoretical estimate, and are several times the theoretical estimate 
for the rapid rotators because of measurement uncertainties [see
additional note regarding influence of the spatial distribution of cluster
members on radial velocity in section 8.3].


     During this study, HE 416, HE 1144, and
HE 1162 were found to be additional candidates for membership and they
have been included in Table 4.  
Stauffer {\it et al.} (1985,1989) obtained BVRI photometry of many
HE proper motion candidates and their photometry was also used to aid in
membership determinations.   Table 5 lists a few bright stars 
that in the past have been 
considered as cluster members that were not in the survey of Heckmann 
{\it et al.}.  

    Fresneau (1980) reanalyzed the HE stars for membership
by recalculating proper motions using astrograph positions of Heckmann 
{\it et al.} (1956) and his own Schmidt plate measures, providing a list 
of `suggested' members of the cluster. 
Trullols {\it et al.} (1989) obtained $uvby-\beta$ photometry
for a number of these and assigned a membership
status to them.  In this study, photometry and
echelle spectra for Fresneau's suggested members were obtained.
Table 6 presents the observations of these suggested members 
(not including seven stars previously considered by Heckmann {\it et al.} 1958).
Table 6 gives the star's name, VBI photometry,
number of observations in each magnitude, BD designation, coordinates from 
Heckmann {\it et al.}, and the membership probability from Fresneau (1980).  The
individual star's membership status on the basis of the VBI photometry is given,
together with the Trullols {\it et al.} determination.  Radial
and rotational velocity information (mostly from echelle spectra
obtained in this study) follow, along with some notes and a final
membership determination. 
The membership determinations of Trullols {\it
et al.} are generally confirmed by the new observations.  Some stars
with questionable membership will require further analysis, including improved
proper motions.  Of the 58 suggested members
 by Fresneau, only 13 appear to be members (Y),
with an additional five being possible members (Y?).


    The AP stars are generally fainter than the HE stars.  Those AP stars 
confirmed as cluster members are presented in Table 7 with photometry
and positional information, and radial and rotational velocity measures
if available.  
Included in the table are the stars AP 8, 16, and 34 which were recovered in
this study 
as proper motion candidates and which were subsequently identified as cluster
members.  Table 8 lists the 14 AP members that were not recovered in
this survey and the reason why each star was not recovered.
Some AP and HE stars originally identified as members by Stauffer {\it
et al.} have radial velocities discrepant with cluster
membership.  For some of these, the discrepant radial velocities were
confirmed with additional (unpublished) observations mentioned in 
Balachandran {\it et al.} (1988), and they are therefore considered
radial velocity nonmembers.  The stars are: AP61, AP68, AP81, AP105, AP111, HE444, 
HE457, HE462, HE493, and HE771.  Additional corrections/additions
to the information published in the Stauffer {\it et al.} are given
in Appendix A.

     Table 9 lists the remaining AP stars which are mainly
proper motion candidates.   Some are
recovered HE stars, but the majority require accurate photometric
and spectroscopic observations in order to determine their membership
status.  None of these remaining AP stars were recovered as proper motion
candidates in the present study.

\vskip .3in
\centerline{7. New Members and Candidate Members.}

     In this section data for the new confirmed members and candidate members
are presented.  These are the proper
motion candidates with membership determinations 
based on the additional photometric and spectroscopic observations.
 
     The proper motion candidates are those stars having motions
within $1\arcsecpoint25$\hfill\break ${\rm cent}^{-1}$ of the cluster motion 
(Figure 3), approximately 715 candidates to the
scanning limit of the Schmidt plates.  Among these were approximately 40 AP
stars and 9 HE stars (not all of which are true 
cluster members).  As is discussed below, approximately 135
new cluster members (and some likely members) have been identified,
together with $\sim 370$ nonmembers and 35 to 40 undecided, possible
candidate members.

     Photometry (mostly in V and I) was obtained for about 590
candidates.  Figure 4 shows the V vs. V$-$I diagram for all the
proper motion candidates observed, with the final membership 
determinations indicated.  Especially for the fainter magnitudes, 
one sees how useful the V$-$I  color is in separating the cluster
stars from the background field star population.  
The AP, HE, and new members form a well-defined
cluster sequence in the diagram (see also Figure 10).  The
photometric errors increase beyond V$\simeq 17$, resulting in 
an artifical widening of the cluster sequence.
The cluster sequence is also broadened by the presence
of binaries, variables, and extremely rapid rotators.  
Errors in the photometry are generally on the
order of $0\magpoint06$ to $0\magpoint08$, increasing to $\sim 0\magpoint1$
among the faintest stars observed (particularly in the V and B magnitudes).
Due to the large number of candidates to be observed, some accuracy
in the photometry was sacrificed.  However, since many of these low-mass
stars are probably variable due to starspots and/or flare activity,
several observations per star are required for magnitudes
and colors having errors on the order of $0\magpoint01$.
One example of variability of a cluster member is
given in Prosser (1991a) where relative photometry of the newly
identified member AP149 is given.

     We allowed for the presence of
binaries and flare stars and for errors in the photometry in our photometric
membership criteria.  
The vast majority of stars lying below the apparent cluster sequence in 
Figure 4 were considered nonmembers based on their photometry.
Additional photometric and spectroscopic data were obtained for stars
falling slightly below the general cluster sequence 
in an effort to determine
their status.  Criteria for acceptance for membership on the basis of 
spectral type are given below.  For those stars with echelle data,
the same membership criteria were applied as were used for the brighter HE stars
(section 6).
A conclusive membership determination was not always
possible, particularly for those stars which fall below but near the
general cluster sequence.   


     Low-dispersion spectra (section 5.1) centered at H$\alpha$ were
obtained for 177 stars, including many AP stars.  
Figure 5 shows a color-magnitude diagram for all stars having spectra, indicating
those which did and did not show noticeable H$\alpha$ emission.  
A V vs. spectral type diagram is shown in Figure 6 for the same set of stars
using the derived spectral type information from the TiO bands. 
Those stars showing definite emission
at low-dispersion form a fairly well-defined sequence in Figure 6. 
Those stars falling below this sequence have spectral
types too early for their apparent magnitudes and would be
considered nonmembers on the basis of their spectral type (allowing
for a $\pm 0.5$ measurement uncertainty in spectral type subclass).
Many of the stars falling below the cluster sequence are late-type
(K, early M) stars,  with consequently weak H$\alpha$ absorption.
Some stars along the cluster sequence labeled 
`H$\alpha$ filled' may be stars having weaker
H$\alpha$ emission that is not strong enough to result in a noticeable
emission feature at this resolution.  H$\alpha$ filled
stars falling below the cluster sequence likely
have H$\alpha$ in absorption but the
contributing factors of low-resolution and low signal-to-noise spectra
did not make identification of an absorption feature possible.

     The presence or absence of
emission itself should {\it not} be used as a sole membership
criteria.  That has not been done here.  The spectral type information
is an effective aid in assessing membership  and the H$\alpha$
observations are used essentially as a confirmation or additional
secondary aid.  It is interesting to note however that in this
sample of candidates observed there were no stars falling on
the cluster sequence beyond V$\simeq 15$ which did not show
H$\alpha$ in emission or filled.
Further analysis of the H$\alpha$ emission strength as a function
of spectral type will be given in section 8.5.

     For most faint (V$\ge 17.5$) proper motion/photometric candidates,
low-\break dispersion H$\alpha$ spectra were obtained at the 
Multiple Mirror Telescope
for the author by Lee Hartmann and his associates and John Stauffer.  
Only the presence/absence of H$\alpha$ emission could be determined from
these spectra. Most of these show noticeable
H$\alpha$ emission (only a couple having H$\alpha$ filled).  Thus,
all the new low-mass members having low-dispersion spectra 
show definite H$\alpha$ emission
(the majority of stars) or show H$\alpha$ filled.  
Those candidates which do not have low-dispersion spectra
but are considered members or possible members are AP 148, 159, 160, 177, and
262.  No selection effect on the basis of the presence/strength
of H$\alpha$ emission has been introduced in deriving the membership
status of the candidates.

     Table 10 presents the results of the above photometry and spectroscopy
observations for those candidates whose final membership determination
indicated that they were members (Y), likely members (Y?), or undecided
(?) candidates.  There are 132 new members and likely members and
16 undecided candidates.  To prevent undue
difficulty in regards to identification, the new members and candidate
members are given the designation of `AP' stars and are numbered consecutively
to follow the lists of Stauffer {\it et al.} (1985,1989).
The columns give the AP number, VBI photometry, number of observations
in V, B, and I, 1950 coordinates, relative proper motions and
errors in $'' {\rm cent}^{-1}$, 
H$\alpha$ equivalent width, and spectral type from low-dispersion
spectra.  These data are followed by the individual membership
determinations for the star on the basis of photometry, H$\alpha$
emission/filled, spectral type, and Hamilton echelle spectra data.
(The H$\alpha$ column
lists Y $=$ emission, F $=$ filled, WA $=$ weak absorption, or
N $=$ no emission.)  A final membership determination
is indicated, together with any additional notes.  The note `MMT'
in Table 10 means that a low-dispersion MMT spectrum at H$\alpha$
was obtained.
Table 11 lists
the radial and rotational velocity data and Li 6707 line presence
for the new AP stars.  
Finding charts for the
new AP stars are available upon request from the author and
are given in Prosser (1991a).


     All those proper motion candidates that were classified as nonmembers
(N) or likely nonmembers (N?) on the basis of their photometry and/or
additional observations are given in Prosser (1991a).  The information
there on the rejected candidates will hopefully be of use to other observers
in rejecting the same candidates that may be recovered in the future.


     It is instructive at this point to look at the distribution
of members, nonmembers, and undecided stars in the original proper
motion diagram. Figure 7 shows the proper motion candidates with their final
membership status indicated.
Notice that the new members extend all the way to the
limiting radius of the sample -- indicating the likely existence of
cluster members beyond those limits.  This was not unexpected
given the typical errors in the proper motions ($1\sigma \sim 
0\arcsecpoint6~ {\rm cent}^{-1}$)
and that the candidate selection area was only slightly over $2\sigma$
in radius.  (As discussed in section 3, the area size was limited
due to encroachment upon the adjacent field distribution about 
$(\mu_x , \mu_y ) = (0,0)$.)   One sees also that the nonmembers
are well distributed throughout the selection area,
with a slight indication that the fraction of nonmembers begins
to increase in the direction towards the field distribution.  The 
distribution of members as a function of magnitude in the proper motion
diagram is discussed in Prosser (1991a).
     
     Figure 8 is the same as Figure 7 but with the nonmembers removed. 
Figure 8 indeed shows that, while the cluster members extend to the 
limiting radius, they are concentrated at the cluster mean motion. 
The proper motion candidates were observed for CCD photometry primarily in
order of their radial distance from the cluster mean motion.  
Of the $\sim 715$ candidates, photometry was not
obtained for approximately 123 stars.  These unobserved stars fall in the
region of the proper motion diagram that is most severely contaminated
by the tail of the field star distribution (i.e. the extreme upper right
of Figures 7 and 8).  It is expected that there are only
a few cluster members within the group of faint stars without photometry.
The loss of these few potential members will not
affect the general analysis in the next section.


\vskip 0.3in

\centerline{8. Analysis of $\alpha$ Persei Cluster Members.}

     Combining all HE, AP, and new AP members and likely members, one finds
that the $\alpha$ Per cluster has a total of about 300 currently known members.
The new observations in this study result
in a `cleaner' HR diagram than previously, as is
shown for the upper main sequence in Figure 9.  A similar color-magnitude
diagram is presented in Figure 10 for the lower main sequence.  While there
remain membership uncertainties among some of the brightest stars
(which were not the object of this study), the refined and
additional membership information enables several characteristics
of the $\alpha$ Per cluster to be investigated.  

\vskip .3in
\centerline{{\it 8.1 Luminosity Function.}}

     Current membership for
$\alpha$ Per extends to V$\simeq 18.8$.  Using a mean reddening of 
E(V$-$I) $= 0.16$ and distance modulus of (m$-$M)$_{\rm o} = 6.1$
(Stauffer {\it et al.} 1989), this limiting magnitude corresponds
to ${\rm M}_{\rm V} \simeq 12.5$  [note: ${\rm A}_{\rm V} =
1.9 \times$ E(V$-$I) $\simeq .30$], reaching a very low-mass
domain ($\leq .25 {\rm M}_{\odot}$). Table 12 gives  
the observed luminosity function for $\alpha$ Per and also for the
Pleiades, corrected for incompleteness
(Stauffer {\it et al.} 1991).  The
observed luminosity function for $\alpha$ Per is shown in
Figure 11, together with the Pleiades distribution scaled to that
of $\alpha$ Per and the scaled field luminosity function (Weilen 1974).
The Pleiades distribution has been normalized to have the same number of
stars as $\alpha$ Per for $1 < {\rm M}_{\rm V} < 3$, while the interval
$4 < {\rm M}_{\rm V} < 6$ was used in normalizing the field distribution
to that of the clusters.

     There is no known bias effect in the present survey which could
cause the `dip' seen in $\alpha$ Per's luminosity function 
at ${\rm M}_{\rm V} = 8$.  Instead, this feature
appears to be a recovery of the `Wielen dip' feature (Bahcall 1986) seen
in Wielen's field luminosity function in the range $6 \leq {\rm M}_{\rm V}
\leq 10$.  The reality of the existence of this dip in the field luminosity
function (compared to Luyten's (1968) smoothed field luminosity function)
has been supported by the investigations of Upgren \& Armandroff
(1981) and Pritchet (1983).   [This feature is also seen
in the analysis of the low-mass membership of IC 4665 (Prosser 1991b).]    
One can see that 
$\alpha$ Per's observed luminosity function does not match
either that of the Pleiades or field -- however there is 
likely to be considerable incompleteness for ${\rm M}_{\rm V}
\geq 5$.  The fact that there is some incompleteness in the
present survey has been demonstrated in regards to the
distribution of members in the proper motion diagram 
(i.e. Figure 7).

    Two methods were used to estimate the amount of incompleteness.  
First, the number of HE members recovered in the present survey was
compared to the
total number of HE members in the magnitude range common
to both samples:  $11 \leq {\rm V} < 12$.  
Allowing for differences in area
coverage between the surveys considered, an incompleteness factor
of $\sim 1.7$ was found. 
Second, the number of AP stars recovered, which extend to fainter 
magnitudes than the HE sample, was compared to the number of
previous AP members.  The present survey recovered about 36 out of
around 50 original AP stars now considered members (Table
7).  This yields a incompleteness factor of $\sim 1.4$ for the present
survey.  On the basis of the 
incompleteness factor estimates and obvious incompleteness
exhibited in the proper motion diagram of new members,  one cannot
reject the idea  that $\alpha$ Per's 
luminosity function is consistent with the distributions
of the Pleiades and field down to ${\rm M}_{\rm V} \simeq 9$
or 10 (disregarding the evolutionary effects in the high-mass
star domain  of the field distribution).  Only further
membership studies will determine if increases in the number
of members by the factors of about two and four for the Pleiades
and $\alpha$ Per respectively are possible at the faintest 
magnitudes in order to bring the cluster distributions
into agreement with the general field.     

     No allowance for the presence
of binary systems has been made in the observed luminosity function
for $\alpha$ Per.  Attempting to correct
the luminosity function for binary systems at this time would
be premature, due to the incompleteness of the survey and
to the errors in the photometry which do not allow a completely accurate
identification for example between likely binary systems and flare stars
on the pre-main sequence.  The Pleiades luminosity function
also did not allow for binary
systems.  Preliminary study of the HR diagram for $\alpha$ Per
indicates that the number of binary systems is not as
large as in many other clusters, and correcting for
binary systems would not significantly affect the above conclusions.

\vskip .3in
\centerline{\it{8.2 Age.}}

     What is the age of the $\alpha$ Per cluster?  Stauffer
{\it et al.} (1985,1989) found that an age of $\sim 5 
\times 10^7$yrs was consistent with the then available
membership data of the lower main sequence.  The large number of new members identified
in this study enables a reanalysis to be made.  VandenBerg's
(1987, unpublished) theoretical evolutionary tracks for
low-mass stars (from 1.0 to 0.3 M$_{\odot}$) were provided
to the author by John Stauffer and used to construct
isochrones for various ages.  VandenBerg's models are
for Y$=0.27$, Z$=0.169$, and ${\rm M}_{{\rm bol} \odot}
= 4.72$.  The following procedure was used to convert the isochrones from
the theoretical (${\rm M}_{\rm bol}$, log ${\rm T}_{\rm eff}$)
to observational (V,V$-$I) plane: (1)
for each isochrone, the vertical displacements
between the theoretical zero-age main sequence (ZAMS) 
and the isochrone were determined over a range of effective temperatures,
(2) the relation 
between temperature and V$-$I was determined (discussed below) and corresponding
V$-$I values calculated, and (3) the vertical displacements
for each isochrone determined at various V$-$I values were
added to an observational ZAMS 
(assuming $\Delta {\rm M}_{\rm V} = \Delta {\rm M}_{\rm bol}$).  

     Two sets of calibrations were employed for the temperature to
V$-$I conversion.
For log T$_{\rm eff} > 3.62$, temperature was converted to
B$-$V using the empirical relation given by Arribas \&
Roger (1988,1989), which are in agreement with
the computed B$-$V values given by VandenBerg for the 0.7-1.0 
${\rm M}_{\odot}$  evolutionary tracks.  The B$-$V value
was then converted to V$-$I using a color-color relation
derived from the field star photometry of Kron {\it et al.}
(1957).  At the lower mass end, log T$_{\rm eff} < 3.62$, a R$-$I value
was determined for a given temperature using the relation 
tabulated in Mould \& Hyland (1976).  The R$-$I value was
then transformed to B$-$V and V$-$I values, again using
the Kron standards.  To make the transition between
log T$_{\rm eff} > 3.62$ and log T$_{\rm eff} < 3.62$ more continuous, a small
offset was added to the B$-$V and V$-$I values for
log T$_{\rm eff} < 3.62$: $\Delta({\rm B}-{\rm V}) = -0.035$ and
$\Delta({\rm V}-{\rm I}) = -0.050$.  The observational
zero-age main sequence (ZAMS) was obtained from a lower
envelope fit to the observed V vs. V$-$I diagram of the
Pleiades (Stauffer 1990), shifted to the distance and reddening
for $\alpha$ Per.  The individual isochrone
displacements were added to the corresponding ZAMS position
at that V$-$I.  The observational ZAMS is not truly a ZAMS at the faint end,
since the Pleiades stars are still contracting.  However,  
this observational ZAMS and 
the solar-metallicity ZAMS for M dwarfs by Stauffer \& Hartmann (1986) 
are in agreement to V$-$I $\simeq 1.9$ (mass
$\sim 0.5$ M$_{\odot}$).  Redward of this value they gradually
diverge,  the M dwarf ZAMS lying only about $0\magpoint15$
below the Pleiades lower envelope curve at V$-$I $= 2.2$.
Hence, the observational ZAMS derived from the lower envelope
Pleiades fit is accurate for most of the domain in $\alpha$ Per 
covered by the isochrones.   Figure 12 shows the V vs. V$-$I diagram for 
$\alpha$ Per with the transformed isochrones and lower envelope Pleiades fit.  
The isochrones are tabulated in Prosser (1991a).

     From Figure 12, the isochrone that provides the best fit to the single 
star pre-main sequence is $8 \times 10^7$yrs.  An age of $\sim 7 \times 
10^7$yrs cannot be ruled out however, given the errors in the current 
photometry, uncertainties in the theoretical models,  
and errors introduced in the transformation of the isochrones from the
theoretical to observational plane. The $5 \times 10^7$yr isochrone in Figure 12
is not significantly different from that plotted by Stauffer {\it et al.} 
(1985,1989),  lending credence to the positions of the other isochrones.  The
main sequence turn-on point associated with the $8 \times 10^7$yr isochrone 
occurs at V$\simeq 13.6$.  Better photometry, low-mass evolutionary models, 
and temperature calibrations will all be needed to enable one to obtain a more
accurate age determination.

     Earlier age estimates for $\alpha$ Per, based on
upper main sequence fitting, yielded an age 
of $\sim 5 \times 10^7$yrs (Mermilliod 1981).  The older
age of $\sim 8 \times 10^7$yrs found here from fitting the
lower pre-main sequence is in accord with other recent increased
age estimates for the Pleiades and Hyades clusters.  
Mazzei \& Pigatto (1988,1989)
have determined an age of $1.5 \times 10^8$yrs for the
Pleiades and $\sim 10^9$yrs for the Hyades age, where earlier
determinations had estimated $7.7 \times 10^7$yrs and
$6.6 \times 10^8$yrs respectively (Mermilliod 1981).  The
apparent age
differences between the upper and lower cluster main sequences
have been used to argue in favor of a sequential star formation
process (i.e. Eggen \& Iben 1988).  However, Mazzei \& Pigatto
(1989) (see also Stahler 1985) recount the uncertainties
inherent in the age determination process and make a plausible
argument against the idea that the difference in age
determinations from the upper and lower main sequences
is particularly meaningful and implies sequential star
formation.  The lower main sequence of $\alpha$ Per does not appear 
to show the presence of a significant age spread ($>> 10^7$yrs).


\vskip 0.3in

\centerline{{\it 8.3 Spatial Distribution.}}

     The earliest studies on the bright members of $\alpha$ Per
comment on the cluster's elongated shape as seen on the sky.
Eddington (1910) remarks that ``The stars are arranged in a kind
of chain and not in the form of a globular cluster.''  
Eighty years later, from the results
of past and present membership studies, we can see if the
spatial distribution of bright members reflects the
general distribution of the cluster as a whole.

      The spatial distribution of members and likely members
is shown in Figure 13.  One immediately
sees that the cluster's distribution on the sky is decidedly
non-circular.  Using known members to define the cluster's extent,
the flattened distribution has a major axis
of at least $7^{\circ}$ and a minor axis of $\sim 5^{\circ}$
projected on the sky ($\sim 20$pc and 14pc
respectively at the distance of $\alpha$ Per).  This 
elongation is parallel to the galactic plane -- as
predicted from theories of tidal deformation.  The tidal radius
of $\alpha$ Per is on the order of
10pc, in agreement with the semi-major axis of
3.5$^{\circ}$ found above; however cluster members can be found
beyond the tidal radius of a cluster (see discussion in Terlevich 1983).
Terlevich also mentions the recent observational indications of flattening
for the Hyades (Oort 1979) and Pleiades (van Leeuwen 1983).
The elongation or flattening shown in this present study on
$\alpha$ Per however is currently believed to be the best observational
confirmation of cluster flattening.  The flattening may 
be due to tidal deformation.  However other possibilities exist,
such as a residual angular momentum component in the cluster
system.  It will require accurate proper motions and radial
velocity studies in order to distinguish the exact cause.

     The spatial distribution of $\alpha$ Per influences
the dispersion in distance moduli and radial velocities of
cluster members.  If one assumes a `depth' of the cluster
of 20pc and a distance of 165pc ((m$-$M)$_{\rm o} = 6.1$), then
the distance moduli of members will vary from (m$-$M)$_{\rm o} = 5.95$
to (m$-$M)$_{\rm o} = 6.22$.  If not accurately accounted for, 
variable reddening will increase the
observed spread in (m$-$M)$_{\rm o}$.  Geometrical considerations of
the cluster's extent, together with its mean radial velocity,
absolute proper motion, and distance,  lead to an expected variation
in observed radial velocity of $\pm 1.5$~km/s about the mean
radial velocity of $\sim -2$~km/s.  This variation should appear as a 
smooth gradient in the mean radial velocity that represents a total
change of about 3 km/s across the cluster.  For
Praesepe, a calculated variation of $\pm 2.3$~km/s, or total change
of $4.6$~km/s, has been estimated (Mermilliod {\it et al.} 1990).
Of course, any membership determinations based on distance modulus
and/or radial velocity should allow for the expected variations
in these quantities.  
Allowances for such variations in radial velocity 
have been made in the membership determinations in this study.
The current membership and radial velocity information is not
complete enough however to allow confident detection of the spatial
variation in cluster radial velocity.

\vskip .3in
\centerline{{\it 8.4 Interstellar Reddening}.}

     Color excesses, E(V$-$I), were determined for late-type
members with low-dispersion spectra.  The analysis follows the
method outlined in Prosser {\it et al.} (1991). 
The spectral type derived
from a low-dispersion spectrum is used to estimate the star's
reddening-free V$-$I color.  A comparison of this with the  
observed V$-$I color gives the color excess, E(V$-$I). 

     The relationship between the derived spectral types and
V$-$I color was determined from the large
sample of Gliese stars observed in the course of the Pleiades
research.  Observed V$-$I colors were obtained for those stars
from Stauffer \& Hartmann (1986) where possible.  Otherwise,
since the Gliese catalog (1969) does not provide V$-$I colors, the
GL stars' R$-$I colors were transformed to V$-$I using the
color-color relation of the Kron field standards used in the
theoretical isochrone analysis.  A mean relation between
pMK spectral type and (V$-$I)$_{\rm {Kron}}$ color for the
field stars was then fit by eye (additional details are in
Prosser 1991a). Only
the stars with pMK spectral type $\ge$ M 0.0 are considered
due to the increasing difficulty of accurately measuring 
spectral types from the TiO bands for earlier classes and due to
the difficulty of establishing an accurate pMK spectral type
vs. V$-$I relation earlier than M0.0 with the present data.

     Individual E(V$-$I) reddenings were determined following
the procedure outlined above for those $\alpha$ Per M dwarfs with low-dispersion
spectra available (Table 15 in Prosser 1991a).  
The derived E(V$-$I) values do 
fluctuate somewhat, occasionally being negative, as would be expected
as a result of the uncertainties in the pMK spectral types and approximate
transformation of these into reddening-free V$-$I values.
>From the 75 M dwarfs with E(V$-$I) values, the mean reddening
is determined to be $<$E(V$-$I)$> = 0.184 \pm 0.001$ (s.d. mean). 
This mean value, although
slightly larger than the value of 0.16 usually adopted for the
cluster, is not significantly different if one takes into 
account the variations
in reddening observed across the cluster.  This mean value
corresponds to E(B$-$V) $= 0.11$ and E(b$-$y) $= 0.08$,
in good agreement with the mean reddenings determined by
Crawford \& Barnes (1974) for the A stars (E(b$-$y) $= 0.076$)
and the B stars (E(b$-$y) $= 0.078$), though their value for the
F stars gave only E(b$-$y) $= 0.060$.

     The variation in reddening across the cluster is shown
in Figures 14 and 15.  Figure 14 shows the locations of bright members,
with reddenings from Crawford \& Barnes (1974) indicated.  Figure 15 shows 
the cluster distribution with the M dwarf reddenings indicated.  
The reddening determinations presented here for the M dwarfs are
only preliminary values because the V$-$I photometry for a fair fraction
of these is not of the highest precision.  
Comparison of the figures suggests that a few 
areas have enhanced reddening: the region to the east (and slightly north) of
$\alpha$ Per itself, and an area around ($\alpha$, $\delta$) $= (49^{\circ},
47.6^{\circ})$  in the south-central region possibly extending
east-west.  The present
data provide a rough indication of the scale and distribution
of the reddening across the cluster; for instance, no general
smooth trend in E(V$-$I) is seen in any particular direction
across the cluster.  The individual reddenings are near the mean
over most of the cluster area, with a few localized high-reddening
areas described above.  Due to the preliminary nature of the
E(V$-$I) values, no attempt has been made here to produce a
reddening corrected HR diagram for $\alpha$ Per.  Such a diagram
however is very important to reduce observational
spread of the main sequence, to provide better identification
of possible binary stars and rapid rotators, and to determine
whether an age spread significantly contributes to any
observed spread of the main sequence.

\vskip .3in
\centerline{{\it 8.5 H$\alpha$ Emission}.}

     In the study of the low-mass membership of the Pleiades
(Prosser {\it et al.} 1991), the H$\alpha$ emission
strength as a function of spectral type was studied using
field stars, Hyades members, and Pleiades members.  That
study is extended here with the younger $\alpha$ Persei members.


      The H$\alpha$ equivalent widths (hereafter `EW') for the
new AP stars are given in Table 10. Additional spectroscopic obervations
for other AP stars are given in Table 13.
As in the Pleiades study, the EW values
are not considered accurate in the cases of weak emission 
($\leq 1$\AA) due to the difficulty in continuum placement.
For comparison with the earlier study, the $\alpha$ Per
equivalent widths have been transformed onto the
Stauffer/Hartmann (`SH') system using
the transformation given in Figure 7 in Prosser {\it et al.}
(1991).  The SH values are considered to be more accurate,
since SH used higher resolution spectra.

     Figure 16 shows the H$\alpha$ EW vs. pMK spectral type
for $\alpha$ Per.  The dashed line is a rough fit 
to the mean upper envelope for the Pleiades cluster
(Prosser {\it et al.} 1991).  From comparison with the earlier study
of the Pleiades, Hyades and field, one finds that
the $\alpha$ Per stars show a significant overlap with the other
distributions.  

     A clearer representation of the data can be made by removal of the 
spectral type dependence seen in Figure 16.  The relative H$\alpha$
strength, $f_{H\alpha}$, is defined as the ratio of the
star's observed H$\alpha$ EW to the EW of the Pleiades upper
envelope curve at the star's observed spectral type.  
Prosser {\it et al.} (1991) show that use of $f_{H\alpha}$ instead
of EW$_{H\alpha}$ should eliminate the spectral type dependence and enable 
a more physically meaningful comparison of emission-line strength between
the clusters.

     Due to the inaccuracies present for spectral types
earlier than M0.0 as a result of the low-dispersion and weak emission,
analysis of the relative H$\alpha$ strengths are restricted
to those cluster stars of pMK types of M0.0 and later.
Table 14 tabulates the $f_{H\alpha}$ distributions found
previously in the Pleiades and Hyades clusters (Prosser
{\it et al.} 1991) along with that for $\alpha$ Per from
the M dwarfs in Tables 10 and 13.  The sample sizes 
are comparable, and observations in each cluster
extend from M0.0 to about M4.5.  The $\alpha$ Per observations
confirm the conclusion that the mean H$\alpha$ emission strength decreases as one
moves to systems of increasing age.  As discussed in Prosser
{\it et al.} (1991), the decline in mean strength is qualitatively
compatible with evolutionary schemes in which both stellar
surface activity and rotation decline with advancing age.
Like the Pleiades and Hyades, the relative emission strengths
in $\alpha$ Per show a marked spread.  The distribution for
$\alpha$ Per does show a noticeable tail extending to stronger
emission strengths than the Pleiades.  The mean relative
emission strength for $\alpha$ Per appears only slightly
larger than that for the Pleiades.  This is not too
surprising considering the relative cluster ages.
The larger displacement in mean
strength between the Hyades and Pleiades distribution is
accompanied by a change in age that is a factor
of 3 to 4 bigger than the age differential from Pleiades to
$\alpha$ Per.

     During this study one apparent flare
star member was detected: AP203.  A MMT spectrum of
the star in 1989 showed tremendous H$\alpha$ emission
(EW$_{H\alpha} \sim 45$\AA).  A second spectrum obtained
in 1990 showed a more typical emission strength (EW$_{H\alpha} \sim 10$\AA).  
This is at present the only known flare star member of $\alpha$
Per.  Tsvetkov and collaborators (Tsvetkov 1991) are currently
planning an $\alpha$ Per flare star survey.  Such
a survey will be very important not only for studying
flare activity in the cluster but also for the identification
of new candidate cluster members. An efficient
flare star survey should improve the
completeness of the low-mass membership in this cluster.

\vskip .3in
\centerline{{\it 8.6 Rotational Velocity Distribution.}}

    In recent years there has been increased interest in the 
study of the rotational velocity
distribution in young to intermediate age open clusters
(e.g. Stauffer \& Hartmann 1987).  The $v\sin i$ determinations from this
study do not alter the previous conclusions of Stauffer {\it et al.}
(1985,1989).  Figure 17 shows the
$v\sin i$ distribution as a function of reddening-corrected
B$-$V, using a mean value of E(B$-$V) $= 0.10$.  Ideally, one would want
to correct each star individually due to the variable
reddening, however that is not possible to do with sufficient
accuracy at the present time.  Small individual changes
however will not affect the general overall $v\sin i$
distribution and do not change the conclusions drawn.
[Note that those stars with $v\sin i \leq 10$km/s have been
plotted at the upper bound of 10km/s in Figure 17.]



     As Figure 17 shows, there is a broad range of observed
$v\sin i$ values at a given color among the low-mass stars.
Stauffer {\it et al.} (1985) mention three possible contributing
influences to such a spread in $v\sin i$: (1) spread in initial
angular momentum, (2) variation in inclination angles, and 
(3) an age spread among the low-mass stars.  As they point
out, it is not possible at present to distinguish between
these; however the increased number of new members found in the
present study will aid future detailed studies on this
issue.  The $\sin i$ distributions can in fact be determined 
through the use of $v\sin i$ and photometric period determinations.
Only a few stars in $\alpha$ Per have reliable photometric
periods however (see Prosser 1991a).  

\vskip .3in
\centerline{{\it 8.7 Binaries.}}

     From past membership studies, several members and candidate
members have been identified as binaries (SB1 or SB2) or
possible binaries, although no periods were determined.  
When many other clusters have been
studied to some extent in regards to their binaries, such as
IC 4665, it is remarkable that a similar study in $\alpha$ Per
has not been previously undertaken.   
However, a study of the binary frequency of $\alpha$ Per's upper
main sequence has just recently been completed (Morrell \& Abt 1991).
Mermilliod (1991) has also provided some additional
SB identifications (Table 4).


     The identification of binaries will be of increasing
importance in the future as the structure of the lower main
sequence is investigated.  Figure 18 shows 
the transition region between main sequence and
pre-main sequence, where a large percentage of the stars
have radial and rotational velocity determinations.  There are
a significant number of stars lying above the main sequence
here.  During this study, four SB2's and at least two SB1?'s
were identified -- each from only one observation.  These
are indicated in the figure.  One sees from the figure that
stars having rapid rotation are not necessarily displaced
from the general main sequence position.  After accounting
for known binaries, possible SB1's, and rapid rotators,
there remains a number of stars lying above the
main sequence in the diagram.  The observational data for
these stars give every indication that they are members.
Reasons for their displacement from the main sequence
could be (1) some (or all) really are binaries which were
not detected from the single observation, or are wide binaries
undetectable at the current resolution limit, (2) the possibility
of inaccurate photometry, (3) stellar variability, or (4) the 
influence of enhanced
reddening for these stars.  The photometry however is believed
to be accurate at this magnitude level, and several stars
have more than one observation for photometry.  While it
is quite likely that at least some are undiscovered binaries,
it is also possible that enhanced reddening comes into
play in some cases.  Those stars which may possibly lie in
high-to-moderate reddening areas are listed in the caption to
Figure 18.  Further observations of photometry, radial velocities,
and reddening are all desirable for these stars.

     During the course of the CCD photometry of proper 
motion candidates, some visual binary systems were discovered in which 
the photometry suggests both stars are members or possible members.
This allowed the survey to be extended to even lower mass stars.  Table 15 
lists the visual binaries with their associated photometry and positional 
information.  Low-dispersion spectra were obtained for AP6C and AP107 
and these do show H$\alpha$ emission (AP107) and H$\alpha$ filled (AP6C).  
Since it appears that the original identification of AP107 by Stauffer 
{\it et al.} was a duplicate identification of AP106, the faint companion
to AP106 has been termed AP107.  AP143C has every indication of being a member,
although it lacks a confirming low-dispersion spectrum.  It
appears to be the lowest mass member of the cluster discovered
to date.

\vskip .3in
\centerline{9. Summary and Discussion}

     An extensive membership survey concentrating on low-mass
stars has been conducted
in the relatively young open cluster $\alpha$ Persei.  A comprehensive data set
of proper motions, photometry, and spectroscopy has been obtained
to identify members.  Over 130 low-mass cluster members have been
identified to ${\rm M}_{\rm V} \simeq 12.5$, almost doubling
the number of known members in this cluster.  

     Analysis of the $\alpha$ Per members has indicated that,
allowing for effects of incompleteness in the present survey, 
one cannot reject the idea that the luminosity function for $\alpha$ Per 
is consistent with
the Pleiades and field luminosity functions to ${\rm M}_{\rm V}
\simeq 9$ or 10.  Inspection of the location of the new members 
in the HR diagram suggests a slight upward 
revision of the cluster's age to $\sim 8 \times 10^7$ yrs.  Improved
low-mass evolutionary calculations are desirable in order to
better compare to the observations.  Perhaps in a few years such
calculations will become available as new opacity information
becomes available.  The lower main sequence observations also
suggest that $\alpha$ Per does not show the presence of a significant
age spread ($>> 10^7$ yrs).

     The present survey has shown that the $\alpha$ Per cluster
is spatially elongated in a direction parallel to the Galactic
plane.  The most straightforward explanation for such flattening
is tidal deformation.  Detailed study of such cluster flattening
in the future should reveal much information about the interactions
between clusters and their environment and provide an observational
comparison to present theoretical modeling.  The distribution of
$\alpha$ Per members over an extended area on the
sky has consequences in regards to the observed range in the values of radial
velocities and distance moduli for cluster members.


     Comparison of photometry and spectral types for 75 M dwarfs has
resulted in a mean reddening of E(V$-$I) $\simeq 0.18$, in good
agreement with earlier estimates.  Some spatial variation in
reddening across the cluster is seen, although the data is not
accurate enough to allow precise reddening corrections to be
applied.  Study of the distribution of relative H$\alpha$ emission
line strength in cluster members confirmed the idea that the
mean H$\alpha$ strength increases in progressively younger systems.
The $\alpha$ Per observations show a range in relative emission
strengths, but with a noticeable tail in its distribution that
extends to stronger relative strengths than observed in the
Pleiades.

     The observed rotational velocity distribution in $\alpha$ Per
was updated with the new observations.  The previous findings by
Stauffer {\it et al.} (1985,1989) have not been altered. 
Continued high-dispersion observations are
needed in order to investigate the morphology of the lower
main sequence and pre-main sequence with respect to binaries and
rapid rotators.  Finally, some visual binary
systems were found to be likely cluster members, including one system containing
the lowest mass cluster candidate member at ${\rm M}_{\rm V} \simeq
13.5$.  


     Does the luminosity function of most open clusters resemble the
field luminosity function for low-mass stars?  Results here have shown
that this possibility cannot be rejected for $\alpha$ Per. 
If one takes this result along with the results of other recent studies 
(e.g., Jones \& Stauffer 1991, Stauffer {\it et al.} 1991, 
Adams {\it et al.} 1983), it is clearly shown
that intensive surveys do identify low-mass members and help remove
the earlier belief that there is a real discrepancy in the luminosity function of
low-mass stars between clusters and the general field.  Some clusters
may exist which do have a steeply declining luminosity function at 
low-masses. However, results of several current surveys have begun to suggest that this
is not the norm.
Given the currently available technology in the areas of astrometry,
photometry, and spectroscopy, there remains much work to be done
in the area of open cluster membership studies.

\vskip .3in

      The author would like to acknowledge the advice and comments
on this program received from Burt Jones (thesis advisor), Bob Kraft
and John Stauffer during its implementation.  Arnold Klemola measured
plates for this program when the author could not be available. 
The author is indebted to Lee Hartmann and his associates and to
John Stauffer for obtaining MMT spectra of several faint candidates.
Support
from the staff of Lick Observatory is also gratefully acknowledged.   
This study was supported in part by NSF Grant Nos. AST-88-03326, AST-90-16521,
and AST-87-20738.


\vskip .3in
\centerline{Appendix A}

     Listed below are some corrections/additions
to the information on previous AP stars published in the Stauffer
{\it et al.} papers.

\hangindent.75in{AP 19:  $=$ HE 622}

\hangindent.75in{AP 28:  RA $= 3^{\rm h} 22^{\rm m} 21.6^{\rm s}$}

\hangindent.75in{AP 50:  $=$ HE 716}

\hangindent.75in{AP 89:  wrong star marked on Stauffer {\it et al.}
chart, AP 89 is bright star north of one marked.}

\hangindent.75in{AP 90:  $=$ HE 389, Fresneau suggested member.}

\hangindent.75in{AP107: this star identified by Stauffer {\it et al.}
is believe to be a duplicate identification of their AP106.  However,
in this study a faint companion lying $\sim 4.5''$ NNE of 
AP106 was found and has been termed AP107.}

\hangindent.75in{AP110: DEC $= 49^{\circ} 51' 18''$}

\hangindent.75in{AP115: nonmember, spectral type (this study) appears too early
for membership in cluster.} 


     It should be noted that Balachandran {\it et al.} (1988) have
given a listing for AP107 which is apparently a duplicate measure of AP106.
In this study, HE1225 is considered to be a nonmember on the basis of
its distance modulus (Crawford and Barnes 1974), duplicity, and radial
velocity. 



\vfill\eject

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\vfill\eject


\centerline {Figure Captions}
\vskip .5in

Fig 1.  Color-magnitude diagram of a representative fraction of
the stars from the Schmidt plate scan.  Some previous cluster
members are identified.  The color-selection is indicated by
the line, below which stars were rejected from further consideration.
The one member falling below the line is AP 20.  Its color
is off because it lies within a ghost image defect on the
Schmidt plates.


Fig. 2. Proper motion vector point diagram from Schmidt plate
measures for regions which are spatially near the cluster center.
The cross at ($+1.9,-2.4$) marks the center of the cluster's
distribution and the dashed box indicates the region within which
stars were considered for further measurement and observation.


Fig. 3. Proper motion vector point diagram showing only the 440
stars kept after the astrograph color selection.  The recovered
members (`AP' stars) are indicated.  The cross at ($2.05,-2.35$)
marks the center as defined by the recovered members.  All
stars falling within $1\arcsecpoint25~ {\rm cent}^{-1}$ from 
this center were considered
to be proper motion candidates needing further observations.

Fig. 4. V vs. V-I diagram for all proper motion candidates
observed, with their final membership status indicated.

Fig. 5. V vs. V-I diagram of those candidates for which
low-dispersion spectra were obtained.  The status of the
H$\alpha$ feature is indicated.

Fig. 6. V vs. pMK spectral type for the group of stars
in Figure 5. The spectral types are on plotted on the system
K3 $= -4$, K5 $= -2$, K7 $= -1$, M0 $=0.0$, M1 $= 1.0$, ...,
through M5 $= 5.0$. Some stars are seen to be too early in
spectral type for cluster membership for their apparent magnitude. 

Fig. 7. Vector point diagram for the proper motion candidates
with their membership status indicated.

Fig. 8. Same as Figure 7, but with the nonmembers removed.
The new members tend to be concentrated near the cluster motion,
however they do extend to the limits of the area under
consideration.   

Fig. 9. Color-magnitude diagram of the upper main sequence
region for $\alpha$ Per.  Approximate spectral type locations
are indicated.

Fig. 10. Color-magnitude diagram of the lower main sequence
for $\alpha$ Per, with approximate spectral type locations
indicated.

Fig. 11. Observed luminosity function for $\alpha$ Per (Table 12),
along with that for the Pleiades and solar neighborhood.
The Pleiades distribution has been scaled to the distribution for $\alpha$ Per. 
The scaled field luminosity function was adopted as an 
relation intermediate
between the field function scaled to the Pleiades luminosity
function, which has been corrected for survey incompleteness
by Stauffer {\it et al.} (1991), and
the field function scaled to $\alpha$ Per, which suffers from
incompleteness effects for ${\rm M}_{\rm V} \ge 5$.


Fig. 12.  V vs. V-I diagram for $\alpha$ Per with transformed
isochrones and Pleiades lower envelope plotted.

Fig. 13. Spatial distribution of cluster members.  Brighter stars
are denoted by larger symbols.  The dashed
region indicates the approximate limits of the present
survey for low-mass cluster members.  An obvious elongation
of the cluster members is seen.  The elongation is in a direction
that is parallel to the galactic plane.

Fig. 14. E(V-I) reddening distribution for the brighter members (HE stars)
with available E(b-y) values from Crawford and Barnes (1974).  The small
dots represent stars which do not have reddening determinations.

Fig. 15. E(V-I) reddening distribution for M dwarfs using
reddening values given in Prosser (1991a).  The symbols are the same
as those given in Figure 14.

Fig. 16. H$\alpha$ equivalent width vs. pMK spectral type
distribution for $\alpha$ Per. 
Those stars with H$\alpha$ in absorption or filled are plotted
with equivalent width $=$ 0.  The mean upper envelope to
the Pleiades H$\alpha$ distribution is indicated.

Fig. 17. Rotational velocity distribution as a function of
reddening corrected B-V color for members and likely members.
Approximate corresponding spectral types are indicated.

Fig. 18. V vs. V-I diagram of transition region between
upper and lower main sequence. Known spectroscopic
binaries and extremely rapid rotators are identified, along
with some other stars falling above the main sequence that
may be binaries. The stars AP 93, 158, 197, 199, and 264
lie in areas of possible high or moderate reddening.

\vfill\eject
\end

