Our motto:  "The determination of ages for individual field stars.....is a field with rich opportunities for large systematic as well as random errors"  (Holmberg et al. 2007)

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......Goals ......
......Project Status ...... 
......Procedure to realize an age ...... 
......Database issues ......
......Age estimators ......

• cluster/association membership
  
• HR diagram
• stellar rotation
• coronal x-rays 
• chromospheric CaII H&K
• lithium absorption
• H-alpha emission
• UV emission
• stellar kinematics
  

......Assigning final ages......

Goals:

•  Most likely age and uncertainty on age [ideal]
•  Lowest plausible and highest plausible age [goal, but i suspect we would be quite unhappy with the dynamic range of the result]
•  Assignment to a logarithmic age bin [necessity though we may want to revisit what those bins should be based on the resulting age histogram.

Status:

after a two-year hiatus, the ages group is back in action!

•        updating database
•        adopting fiducials
•        refamiliarizing ourselves with age assignment infrastructure
•        working on age calibration equations
•        setting procedure for adopting final ages
  

link to current paper figures [not updated since 2005]

link to ages derived from various techniques [not updated since 2005]
figure illustrating age vs age correlations. ACTION: assess offsets and correlations with color; improve the various age calibrations

link to ages for "IRAC paper" targets
link to ages for "first-look" gas targets

• For individual FEPS stars, first decide on fiducial values for each relevant age indicator.  Where multiple entries exist in database, can either adopt values from single references/sources in  priority order, or calculate mean/median and dispersion from all available values.  Outcome of discussion was that for mostindicators should NOT average measurements with error taken as dispersion in ensemble comparison between sources, but should have priority ordered references based on spectral resolution and trustworthiness.  Documentation of decisions for individual indicators appears below.
ACTION: Needs to be finished in database

• Adopt relations between age diagnostic and stellar age derived from examination of open clusters. Need to worry about mass stratification issues in deriving calibrations. Evidence of small offsets in calibrations based on resulting age-age correlations. ACTION: Revisit LAH cluster calibrations.
• Apply calibrations to fiducial values of age diagnostics for FEPS sample.
• Test results:
• calculate average/median and dispersions in ages derived from different methods
• assess discrepancies between age diagnostics.
• do clusters members have "correct" ages derived from the age indicators we hope to apply to the field stars?
• establish applicable range in the observable for each age technique
• Adopt an algorithm for assigning ages to individual stars.
• Estimate a best age or age range.
• Estimate uncertainty.
• Populate FEPS database with these values
• Put into a FEPS age bin.
ACTION: Finalize existing infrastructre for carrying out these steps.

Database issues:

Status:  

• Much age-relevant info in FEPS database including large, uniform catalogs as well as single measurements.
• Information from the "comments" section for individual stars has made it into the "tables" section, despite difficulty in getting data entered due to hetergeneity of entries.  Competent undergraduate went through files created from FEPS Database comment fields and made FEPS Database upload files. These were uploaded along with entry of relevant bibliographic information. 

Data actions:  

• We have to be mindful of  SB's affecting velocities and perhaps lithium.  The Ncompanions tag in the database is not particularly complete.  The WDS info has been uploaded as well as Metchev's thesis work, but there is another relevant catalog from USNO which has not.   ACTION: Check with NStED folks.
•  Southern echelle data from  CTIO and MIKE is not yet included ACTION:  EEM to reduce/analyze his data!
• Upload Holmberg et al 2007 which is an update of Nordstrom 2004 (Teff, Fe/H, HRD ages)
  
• Should hire an undergrad to simply play around with stellar properties in FEPS database and make plots.  Probably too late for this.
• Fiducial settings still to be made:  
• for distance:
• for log T:
• for log g:
• for Fe/H: use Valenti/Fischer with first priority
• for RV: calculate weighted average and uncertainty using all available values in which there is confidence.

Relevant # of FEPS stars:  ~130
                                             22 - Hyads,  20 - Pleaids,  13-  Alpha Per,  5 - IC 2602,  
                                             14 - LCC,  23 - UCL,  17 USco,  7 Cor Aust

Status:

• "GOLD STANDARD" age indicator.
• For both "traditional" open cluster members and for more newly appreciated associations/groups, the age assignments in the FEPS database are now those of the cluster.  Old designations such as Cas/Tau have been removed.

Data actions:

• revisit open cluster ages -- Alpha Per and Pleiades still controversial after all these years. DONE by stauffer and mamajek
  

Analysis actions:

General Concerns:

• Should probably distinguish between secure clusters and less secure moving groups in our final weighting scheme.
  

Relevant # of FEPS stars: ~90 Pre MS,  ~240  MS, and 2 bona fide Post MS

Status:

• "SILVER STAR" age indicator
• Tycho BV and 2MASS JHK photometry, and Hipparcos distances available for most  stars.
• EEM has updated distances for stars which were formerly below the zams.  See parallax memo for some tests.
• JMC has calculated kurucz model luminosities and kurucz model temps which we are adopting for now. ACTION: Check with John post-sept 2007 regarding status of promised update to these values.
• LAH has interpolated masses and ages for various tracks.
  
• Should we make use of assembled log-g information?
• We like methods that also reproduce the cluster turnoff ages:       

                                log(age/yr)   age(Myr) 
                      LCC                           17
                      IC 2391   ~7.71          52                
                      Pleiades  ~8.01         102       
                       figure illustrating post-main sequence tracks                                                                                                  

Data actions:  

• there are still some sources without fiducial temperatures (a few cluster stars and 3 sources added to source list in 2003 June):
  HII 152
  HII 1101
  HD 43989
  HD 45270
  HD 72687
  HD 115043         ACTION: ASSIGN THIS TASK
• there are a few stars that perhaps need their distances revisited.   ACTION: VERIFY IF 1-3 BELOW ARE COMPLETED.  4 IS NOT(?)
  1) HD 106772. Eric has some notes that suggest we should adopt the main sequence distance and I think I concur.
  2) HD 219498. Same category as the above in terms of inferred age from activity indicators being inconsistent by 1.5 orders of magnitude with the HRD location inferred from our assumed distance.
  3) Some of the Cham region stars, espeically RXJ......-7735
  4) There may be others that are not obvious outliers in the HRD but whose distance reference is "FEPS".  There are 81 stars with a "FEPS" distance reference that are not included in Eric's memo.  We should see what we really believe from the kinematics, and consider at least entering the main sequence distances as one possiblity  JMC: We also have the angular size from the Kurucz model fits. In principle we can look for a consistency check between the distance, angular size, and age, although I suspect there will not be enough dynamic range in the stellar radii vs. age to make this useful.
  

           

Analysis actions:

• Mamajek:

           I have a program that makes monte carlo realizations of HRD positions,    
           interpolates their ages and masses from tracks, and then quantifies the
           mean, median, and confidence intervals (use 68%?) for the ages and masses. 

• Need to test ages/masses derived from different tracks for these solar-type stars.  Which do we use?
• Need to address degenerate overlap betwen PMS and MS tracks.  In most cases other age indicators should pick up the slack.
• Should we develop an empirical plane  Mv / B-V and/or Mk / J-K (avoiding the famous stauffer bluing effect) isochrone interpolator that can handle errors in distance, photometry, etc. ?    Stauffer: my preference would
      be to plot the observables and compare them to isochrones that
      either are natively in colors and mags or that we convert to
      colors and mags.   At least the Berkeley model is to go that
      route - plot the objects we observe in the sky in the units they
      are observed as much as possible, and where necessary transform
      models to that plane.  Small study of using observables to define CMD locations vs. using LogL, LogT from JMC database. 
• ACTION:  JMC to try fixing Av for Pleiades, Alpha Per and ? in order to see how big an effect this is on L and T.   
• ACTION:  Can John report a f_bol w/ error from the fit between the photometryand the Kurucz models? It would seem that this may be better than using  individual colors and magnitudes which may have systematic effects (see Stauffer+ 2003).
  

General Concerns:

• effects of binarity, making stars appear younger
• effects of x-ray selected sample
• PDS66 was a star of some discussion.  is the isochronal age (17-23 Myr) of LCC appropriate, or is it younger as suggested by other diagnostics and its own particular HRD location (7 Myr)?   discussion
• HD8907 was also discussed at length.   HRD relevant info for HD8907* appears in the directory of  stauffer plots
• HRD ages older than 20 or maybe 30 Myr need to be viewed with heavy suspicion as the
  track interpolation routines do not do well here, especially for stars in our mass range
• method should be applied only when known that star is likely young enough to be pre-main sequence.  it is very easy for stars that are really 250 Myr-old to masquerade as 30 Myr-old stars.   alternately, could derive for all stars and then weight this age quite low when combining ages from different methods.  
  
• several studies have published ages for feps targets based on post-ms isochrones which are inappropriate.
  
• We do appear, however, to have several bona fide evolved stars in the sample. These include 2 of the 3 objects that were put on FEPS because they are known planet stars, 1 (hd 157664) that was put on FEPS because it was an IRS calibrator, at least until we pointed out from our AO data that it is a very close equal mag binary and Watson dropped it. The evolved stars were identified by comparing their pre-main sequence isochronal ages with the activity/lithium/rotation ages.

Relevant # of FEPS stars: ~300 stars with vsini values, though 40 are upper limits.  
                                             101 stars with periods !!

Status:

• still working on implementing fiducial values.  intended prioritization:
• Raboud
• Queloz98
• Soderblom98
• White07 (many upper limits)
  
• fiducial cluster vsini data assembled
• Fit function to median vsini in BV range of FEPS targets - surprise, it's t^-1/2!  there may be a systematic offset in this calibration at older ages as inferred by comparison to other age indicators.
• Large, uniform set of periods from greg henry added to database.   figure characterizing the data.  remarkably, the periods do not fill in any information at all on the low vsini tail.....
• For kicks, i then compared the period and vsini data and attemped to derive inclination angles, as illustrated in this figure . the two outliers are HD 199143 at the highest vsini and slow period (6 days) and HD 38529 at the slowest period and moderate vsini. These stars are not unfamiliar to the group.
• Mamajek has written a memo performing the "gyro age" calculation prescribed by Barnes (2007).

Data actions:

• need scrutiny of vsini data in the database   These stars in particular may need updates.  what is a believable lower limit from e.g. nordstrom 204?  ACTION: ASSIGN TASK!
• The Paulson et al 2003/2002 values of Hyades vsini / R'HK are not entered uniformly.  
  
• change remaining P60 vsini upper limits listed as fiducial values to measurements from other references.   One exception for vsini is HII174, where stauffer is sure the published literature has too small a value. 
  
• need Mamajek CTIO+MIKE vsini values for southern FEPS stars.
• make sure final henry (private communication) periods are in the database rather than preliminary versions.  ACTION: LAH

Analysis actions:

• decide how to handle vsini upper limits in analysis
• incorporate soderblom etal 93, terndrup et al 2000, soderblom and mayor UMa work for cluster analysis  ACTION: ASSIGN THESE
• calculate vsini av/med for de la Reza 2004 compilation of TWH/BPic/TucHor to be added to cluster analysis
• check for usesful info in barnes 2003 in addition to scrutiny of barnes 2007
• Could turn the vsini calibration issue around by converting vsini's to periods ( v~sini = 2 pi R* / period * pi/4) and just adopting Barnes.
  
• Stauffer suggestion:
  
  * create a model open cluster, whose vsini distribution
  is fiducialized as being equal to that of ScoCen or IC2391
  at their respective ages.
  
  * develop a parametized model of angular momentum evolution -
  a sun-like wind, whose dJ/dt saturates above a critical
  velocity; spinup due to contraction while on PMS tracks;
  possible feed up of J from the radiative core.
  
  * evolve the model forward in time, and tune the parameters
  so that you get as good as possible match to the vsini
  distributions of the open clusters I've given to you.
  
  * then, populate a database via a monte carlo program with
  vsini's as a function of mass and age.
  
  Then, for any given program star, draw 500 stars from the
  database with the same mass (B-V color) and vrot (+/- errors)
  as the program star.  Each star from the database will have
  an age associated with it.   Calculate the mean and sigma
  of those ages, and that is what you associate with our program
  star.
  
  Admittedly, that is a non trivial amount of work to implement,
  and it possibly suffers from serious non-uniqueness problems,
  but it has the advantage of not "throwing away" the information
  contained in the actual vsini distribution at each observed
  age.
  
  John
  

General Concerns:

• vsini shows a lot of scatter especially at young ages, as is well known.
• concern about mass dependence even over small range of B-V=0.5-0.8 for feps targets.
  

Relevant # of FEPS stars: 271 from a large and relatively homogeneous database: ROSAT


Status:

• mamajek has produced a FEPS database memo on x-ray fluxes.  one open question is how extinction is treated.
• carpenter had f_bol computed from kurucz fits and Lx/Lbol now present in database
• fit function to median Lx data for clusters taken from the literature.

Data actions:

• 
  

Analysis actions:

• improve on assembled cluster median/mean values by adding IC4665 (Giampapa et al 1998), NGC 2547 (JT 1998), NGC 2516 (J97), Blanco 1 (Micela etal 99), NGC 6475 (Prosser etal 95, JJ 97), Praespe...also checking field stars: Markov? Schmidt&Liefke 2004?.   also new data on young end from Preibisch on ONC and XXXX on Taurus.         

• the X-ray/bolometric ratio log(Lx/Lbol) would seem to be a
  better index of activity...  an activity "efficiency" rather than a
  straight-up flux. Using Lx would seem to be analogous to using the
  luminosity of the Ca H & K emission lines, rather than normalizing it to
  the stars luminosity.  ACTION:  assemble Lx/Lbol data for clusters
• compare Lx and Lx/Lbol to age and vsini/period (B-V segregated)
• can use Pizzolato 2003 compilation for field stars as a check of methods

General Concerns:

• how to treat xray upper limits?
• variability, especially bias related to catching objects in flare state.
• There is potantially a blue/red (based on B-V quartiles) split in the Lx data.
  
• x-ray evolution at young ages is minimal due to saturation.
  
• is it worth converting logLx/Lbol to R'HK?   Stauffer: my vote is not to try to combine Lx/Lbol and CaHK.  there is
    no certainty that they scale exactly with each other.   New Mamajek evidence suggesting we should consider this more seriously.
  

Relevant # of FEPS stars:   258 stars!                                  

Status:

• Mamajek preparing a separate publication on the age-activity relation using open cluster data assembled from the literature and converted to common system.
• Every FEPS stars with R'HK in the database now has a fiducial value set.
• Have adopted fiducial R'HK values in the following priority order, largely based on the number of measurements going in to any average values quoted in the paper.   ACTION: LAH to finalize psql commands for database  DONE (thanks john!)
•                  Baliunas et al 1996        
•                  Duncan et al. 1991       
•                 Wright et al. 2004         
•                  Henry et al. 1996         
  
•                 White et al. 2007         
  
•                 Gray-Nstars (Gray06)         
  
•                 Gray03             
  
•                 Soderblom00             
  
•                 SoderblomMayor93  
  
•                 Soderblom98             
  
•                 King03             
  
•                 Tinney et al. 2002         
  
•                 Silverstone et al. 2000     
  
•                 Laws03             
  
•                 Rocha-Pinto04
•                 a few other random papers with 1 FEPS star each             
  
  
  
  

Data actions:

• Some BV photometry has large errors or is inaccuracte and these stars need to have fiducial photometry replaced..  ACTION:  Volunteer to go through these and set other photometry  as the fiducial
• need to keep an eye on  Gray/Corbally  nstars project web page for most recent measurements; many more feps stars are in this sample but thusfar only 2003 and 2006 papers have been entered.  ACTION:  check feb06 email from MRM to see if any new information
• should calculate average of and dispersion in R'HK for individual stars.   
• dump strassmeier 2002 RHK values since they are not R'HK.

Analysis actions:

• understand color correction (e.g. to B-V=0.60 as advocated by Soderblom 1991 or Paulson et al 2002, both for Hyades samples) the slope of which appears to depend on age (!!)
• include cluster median and mean values, as for vsini exercise, and make sure only solar-type stars are used or appropriate color corrections are applied
• have R'HK for 97 hyads from soderblom table, 16 of which are feps objects, but remainder can be used in calibration and understanding calibration.
• include new UMa data from King 2005 in calibration  ACTION: Mamajek
• plot individual R'HK values vs color/temp, so as to mimic vsini and lithium plots  ACTION:  Hillenbrand
• see if PP04 data on ngc3680 and ngc4651 can be added by converting F'K  to R'HK using Hyades or M67 stars in common with other surveys. this should be something like F'K = FK(1-R_phot/RHK) with R_phot = RHK - R'HK.   DONE by DS; however, the results appear inconsistent with the generally accepted R'HK vs age relationship.  ACTION:  Soderblom

General Concerns:

• variability, possibly higher at younger ages where the age-activity relationship is least well calibrated.
• utility below 100  Myr where the activity-rotation correlation disappears.   -4.35 seems to be the upper activity limit for deriving an age.
• pre-/post-main sequence applicability.   Mamajek comments:                                                                           
• The calibration of the activity-age relation is for
  main sequence stars (although we are stretching it to
  pre-MS for FEPS!). David S. (1991) included some stars in his
  calibration that were slightly evolved (late F stars), but not ones that
  have almost reached the base of the giant branch (as HD 38529 is). I'm
  sure someone could do some sort of empirical R'HK vs. age relation
  for post-MS stars, but as far as I know - none exists (perhaps David could
  comment on this?).
  
  Some additional empirical proof that the R'HK vs. age relation is
  inapplicable for evolved stars is Fig. 6 of Wright et al. (2004).
  It shows that the majority if very inactive stars (logR'HK < -5.1) are
  simply bloated, evolved slow-rotating stars. Rather than being ~8
  Gyr-old MS stars, as inferred from their activity levels, they are more
  likely more massive, evolved ~5 Gyr-old stars (I came up with these
  numbers assuming two cases: a MS star with B-V=0.7 with R'HK = -5.1,
  which gives an activity age of ~8 Gyr with most people's calibrations,
  and a post-MS star with B-V=0.7, Mv=3.5, which is roughly the loci of the
  low-activity stars in Fig. 6 of Wright et al. 2004, which on solar-Z
  tracks implies an age of ~5 Gyr. Hence, taken at face value, the
  "activity age" of the star (assuming its MS) would seriously overestimate
  the true age of the star (if its post-MS). I think this is what is going
  on with HD 38529.
• the weight of history.
  

Relevant # of FEPS stars:  ~315!

Status:

• here is a list of lithium-relevant comments that were uploaded. 
• still working on implementing fiducial values.  intended prioritization:
• Soderblom93
• Pal60 (current default in most cases as literature comparison is +/-30 mA; see White et al 2007)
• others
  
• The number of FEPS targets which are more Li-rich than 95% of members of the following clusters are:
  Name              Age N_FEPS(1) N_FEPS(2)
  IC2391+2602  53   31        0
  AlphaPer        90    55        0
  Pleiades        125    72        0
  M35              175  117      37
  M34              250    66        2
  Hyades          625    52    114
   where N_FEPS(1) are the number of stars with Teff in the range actually
  probed by Li studies in the literature, and N_FEPS(2) is number that are
  more Li-rich than a "good extrapolated fit" (this is for stars with Teff
  values outside the range probed for a given cluster, or where a lot of
  upper limits preclude the calculation of an appropriate polynomial)

Data actions:

• need to choose fiducial values in cases where more than one measurement present
• 
  
  

Analysis actions:

• MAMAJEK:  I can take the lead on the Li, as I've accumulated a lot of the
  cluster data and am very interested in putting something together that
  spits out an age with "believable" error bars. I don't think it would be
  appropriate to describe the whole thing in the FEPS age paper, other than to cite a Mamajek+ (in prep). 
• Memo from 14 November 2004 is a good start on description of the method.
• Could add in other clusters:  ngc 752 (sestito et al 2004), Coma Ber (Ford 2001), ngc 6495, blanco 1, ngc 2451, ngc 2547, ic4651, ngc3680 (Pasquini et al 2001), M67, ngc188 (randich et al 2003). 
• update calibration data based on new jeremy king on UMa
• Do we have all the data mentioned in Soderblom 1999, Table 1 and Barrado et al 1997?
  
• should perform fits only over FEPS temperature range instead of over full range since this can bias method depending on how peak is fit
• test derivation of lithium limits from traditional lower bound techniques as a complement to Mamajek's best +/- 1sigma method.
  
• show B-V or temp limits of FEPS range on plot as in vsini plots
  
• present mean and median vs ages as in vsini plots
  

General Concerns: 

• in P60 data we have not applied any correction for FeI 6707.4 A which is a 10-20 mA effect for GK spectral types.
• treatment of upper limits.  at what age do upper limits become a source of bias in the mamajek technique since not including them means that a given field star must have more lithium than the average cluster member to have the age of that cluster.
• lithium ages show more scatter than other indicators
  

Relevant # of FEPS stars:  ~230
                                            main reference is P60 data since we have not tabulated this quantity from the literature.

Status:

• HELD IN LIMBO FOR NOW.  
• Available literature is quite scattered, but should be able to anchor a relationship for solar type stars with open clusters.
  
• For Pleiades
• Soderblom et al 1993
• Hodgkin et al 1995
• For Hyades -
  
  
  * Campbell - 1983, AA 123, 89 - shows that the Hyades G dwarfs
        have partial "filling in" of H alpha compared to old G dwarfs
  * Cayrel, Cayrel and Campbell - 1985, AA 146, 249.  Illustrates that
     can get good Teff's even for Hyades stars from H alpha profile
     shape.  Fig. 9 shows difference between Hyades G dwarfs and
     field G dwarfs in terms of H alpha profile shape.
  * Stauffer et al - 1991, ApJ 374, 142.  Provides H alpha equiv.
     widths for G, K and M dwarfs in the Hyades (G5 and later probably).
     Probably still suffers from where to put the continuum.
• For M67 -
• Perhaps, as for UV, this is useful only as un upper limit indicator on ages.

Data actions:

Analysis actions:

• figure of EW(Ha) vs B-V from P60" data.   plot made but fit not yet done.
• should emulate Mamajek 2002 vs Lyra & de Mello 2005 analysis
  

General Concerns:

• not clear how to relate to age
• likely variability

Relevant # of FEPS stars: none at present

Status:

• WE ARE PUNTING ON THIS AS A QUANTITATIVE AGE INDICATOR
• KEEP AS QUALITATIVE INDICATOR, USED TO SET UPPER AGE LIMITS FOR KNOWN UV ACTIVE STARS
•  COULD ENVISION A GALEX INVESTIGATION BUT NOT ON NEEDED TIME SCALE

Data actions:

• incorporate Galex photometry from AIS, when released
  

Analysis actions:

General Concerns:

Relevant # of FEPS stars:  now 286 stars with radial velocities!

Status:

•  COMES INTO AGE DISCUSSION IN SEVERAL WAYS                        

                                 - 1) ALL FEPS SOURCES SHOULD BE DEMONSTRLY "YOUNG DISK" STARS
                                 - 2) KINEMATICS ALSO USED TO CONSTRAIN MEMBERSHIP IN MOVING GROUPS
                                 - 3) KINEMATIC DISTANCES FEEDS INTO HRD

• IN SUMMARY, NOT A QUANTITATIVE AGE INDICATOR BUT SOMETHING TO WHICH WE ARE PAYING ATTENTION 
• Mamajek performed a sanity check on his kinematics codes by testing whether the 24 FEPS pleiades members run through his convergent point code came out as members.  All is well.
• Mamajek has written a memo describing kinematic distance methods.

Data actions:

• Mamajek to enter kinematic distances from his thesis work into database. DONE.  These are adopted  as fiducial values
  unless:
  a) there is a trigonometric parallax value with smaller error bars
  b) they clearly belong to a cluster/association with known distance
• here is a list of vrad comments someone should ensure are uploaded.
• should make some notations when rv is variable, indicative of binarity (e.g. 40419 57271)
  
        
  
  

Analysis actions:

• Mamajek:
I also have a separate set of constraints on the age vs. R'HK relation that we haven't looked into: kinematics [big surprise]. Long story short, I have assembled a catalog 1258 unique solar-type stars with UVW space motions (from cross-referencing the digitized catalogs of Henry+ 1996, Wright+ 2004, and Nordstrom+ 2004; it was nice, i didn't have to calculate a single UVW vector or R'HK value!). There are excellent models which fit the age vs. space velocity dispersion for evolved stars from the Hipparcos catalog. It is trivial to measure the velocity dispersions of the 1258 FGK R'HK stars with UVW vectors -- and for each subsample, estimate the age from the best fit models. The initial attempts at this look promising .. i.e. the inferred ages for a given bin of R'HK values are near the best fit regression lines for R'HK vs. age that we have so far.
• Mamajek:

I still need to calculate a few more group space motions
(for T associations with no published UVWs) before calculating "final"
membership probabilities for FEPS targets. I'm also trying to figure out
if/how to weight membership probabilities (what do you do when you have
a star that has a high membership probability to several groups? is a high
membership probability even useful at that point?).