Can amateur observers discriminate the core of dense globular clusters like M3 and M15?

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Can amateur observers discriminate the core of
dense globular clusters like M3 and M15?

• Rodney Howe
• AAVSO SID Analyst
• Strikis Iakovos - MariosHellenic Amateur
  Astronomy AssociationElizabeth Observatory of
  Athens
• Ido Bareket???? ??????? ???? ??????http//www.ba
  reket-astro.comBareket observatory, Israel
• Stouraitis DimitriosHellenic Amateur Astronomy
  AssociationGalilaio Astronomical Observatory

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Video of Globular Cluster M3Large file download
16MB

• Note the variable stars scattered around the
  cluster!
• http//ncastro.org/Contrib/Howe_R/M3.wmv

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Or, perhaps use a Period Luminosity ratio for RR
Lyrae stars

• A correlation between the periods and
  mean luminosities of Cepheid variables. The
  period-luminosity relation was discovered by
  Henrietta Leavitt in 1912. The longer a Cepheid's
  pulsation period, the more luminous the star.
  Since measuring a Cepheid's period is easy, the
  period-luminosity relation allows astronomers to
  determine the Cepheid's intrinsic brightness and
  hence its distance. If the Cepheid is in another
  galaxy, the Cepheid's distance gives the distance
  to the entire galaxy. 

period-luminosity relation

                                                                
http//www.daviddarling.info/encyclopedia/P/period
-luminosity_relation.html
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Classical method for determining cluster
distances.

• Luminosity Distances
• Indirect distance estimate
• Measure the object's Apparent Brightness, B
• Assume the object's Luminosity, L
• Solve for the object's Luminosity Distance, dL,
  by applying the Inverse Square Law of Brightness
• Apparent Brightness is inversely proportional to
  the square of the distance to the source
• We call this the Luminosity Distance (dL) to
  distinguish it from distances estimated by other
  means (e.g. geometric distances from parallaxes).
• The only observable is the object's Apparent
  Brightness, B. The missing piece is the
  luminosity, (L), which must be inferred in some
  way.

http//www.astronomy.ohio-state.edu/pogge/Ast162/
Unit4/cosdist.html
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• Method
• Build up a calibrated H-R Diagram for nearby
  stars with good parallax distances.
• Get Spectral Type Luminosity Class of the
  distant star from its spectrum.
• Locate the star in the calibrated H-R Diagram
• Read off the Luminosity
• Compute the Luminosity Distance (dL) from is
  measured Apparent Brightness.

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Measure field RR Lyrae distances by parallax
(these two images are 7 years apart!)
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RR Lyrae Stars, Horace A. Smith, 1995, Cambridge
Astrophysics Series
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Amateur Astronomers have no consistent way of
defining the core of a globular cluster, thus
differentiating the core from the periphery. This
segregation is important for characterizing the
gravitational dynamics of the cluster,
particularly in the core.
The periods of RR Lyrae variable stars introduce
segregation errors due to their inherent
variation. Current core sizing is a function of
the luminosity versus distance from the core
center. However, once in the core, the variations
in the RR Lyrae stars introduce significant error
in the luminosity determination. Hence, by
characterizing the RR Lyrae quantities and
oscillation periods, we can reduce the core
dimension error.
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How do we discriminate the core?

• (Ido Bareket)
• One approach for better identification of the
  'core' area vs. the other outer region areas can
  be done by finding any potential correlation
  between the angular size of the target - and its
  standard deviation of the stars, VS. their
  distance from the core.There may be another
  more elegant solutions, but I don't aware of
  such. I believe that it will be easier to do this
  manually though. At least with these small lists
  of targets.

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Outer region cluster RR Lyrae phases from stellar
pulsation sources

• Iakovos writes As for the M3 Globular Cluster
  images I did a random selection of about 100
  stars in the outer parts of the cluster images
  and did the photometry profile in just one window
  ... Then I started to erase those which did not
  have an RR-Lyrae type of variation and this is
  how I finally stopped to those 20 stars ...
• http//www.aavso.org/vsots_rrlyr

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Cutting up the cluster to identify
period/luminosity ratios
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But, which Pixel Value should we choose? Perhaps
the Full Width Half Maximum (FWHM)?
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FWHM is just the yellow part of the flux density.
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Or, by cutting up the images by visual
inspection 32 images for 3 nights of M3 (Ido
Bareket), 46 images one night of M15 (Iakovos
Strikis)
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And then compare magnitude (digital number)
differences between outer image regions (more
dark sky) and inner regions (no dark sky)
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Cut right to the core! To follow the period
changes over time.
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However, core Period/Luminosity concerns, with
amateur telescopes and cameras

• Iakovos writes As for the decrease of the flux
  density of the M15 core ... I also think it is
  not real, and I believe that it is caused from
  the camera stabilization .... All cameras need
  about 11/2 hours to be thermal stabilized... If
  I start to image before that time the linearity
  of the camera (and sensitivity) are going to be
  changed until the camera gets thermal stabilized
  ...

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How about treating the cluster as just one star?
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Tom Krajcis observatory for AAVSO
http//picasaweb.google.com/tom.krajci/Autoscope22

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October, 2010 277 images over 4 nights of M15

• K28 (Krajci-28) is a 28-cm Celestron C-11 located
  at the Astrokolkhoztelescope facility near
  Cloudcroft, New Mexico (UT-7). This telescope was
  donated to the AAVSO by Tom Krajci.
• (K28 is a Celestron CPC-1100 fork mounted 11-inch
  Schmidt-Cass, using an ST-8 at 1x1 binning. 
  Image scale is approx. 1.056 arcsec/pixel, and
  frame FOV 27 x 18 arc minutes.)

http//www.aavso.org/aavsonet
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Also, Johnson-Cousins filters U,B,V,R,I were used
in previous work for visual inspection. Now Sloan
filters u,g,r,i,z are being used in the one star
approach.
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How might we do photometry and treat the cluster
as one star, and with a mix-match of filters?

• Photometric Standard Fields (Stetson Catalog)
• Here is a current list of my photometric standard
  fields.
• U,B,V,R,I give the number of standards in each
  filter, where a standard has at least 5
  observations made under photometric conditions
  and sigma(mag) lt 0.02 mag in a given filter.
• The coordinates given are the (2000.0)
  coordinates of the field center. This may be
  followed by field size in arcminutes (RA, Dec).
• Each field is represented by three files
• 1. .pos -- The (2000.0) positions of the stars
  in (a) RA, Dec in decimal degrees (b) RA, Dec in
  hexagesimal HH MM SS.S sDD MM SS (c) offsets in
  arcsec from a given reference position (d)
  position, in pixels, in the image described
  below.
• 2. .pho -- The photometric data mag,
  sigma(mag), N(obs) for U, B, V, R, I, plus a
  measure of variability sigma(1 obs).
• 3. .fits -- A composite image of the field. All
  images consist of short integers, and have
  increasing East and y increasing North. The scale
  is an integer number of pixels per arcsecond,
  usually two pixels per arcsecond (0.500
  arcsec/px) but sometimes, depending on the
  seeing, three or even four pixels per arcsecond.
  The scale factor (number of pixels per arcsecond)
  is the third number in the header keyword OFFSCA.
• If the field size is given, that means the field
  is ready now the others are in various stages of
  progress. Feel free to encourage progess on any
  fields of particular interest to you.
• Field RA Dec RA size Dec
  size UBVRI positions
  photometry image
• NGC707821 30 08.312 11 4424.332.275497813080258NG
  C7078.posNGC7078.phoNGC7078.fits.gzG26_721 31 00 -
  09 47 11111

http//www3.cadc-ccda.hia-iha.nrc-cnrc.gc.ca/commu
nity/STETSON/standards/
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Well have to use a photometry software package
that can overlay all 243 Stetson stars onto the
277 October (4 nights) M15 images VPHOT is an
AAVSO online photometry data reduction tool which
can do this.
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VPHOT is used to create instrumental magnitude
comparisons for each of the K28 M15 Sloan
filtered images.
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Perhaps there is a color (g- r) index that can
help discriminate what is going on in the core of
these globular clusters?
Midx ((g-r) / (gr))
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These are Stetson star color plots over time
(Right Accession) and sorted by the
Johnson-Cousins Blue filter. V and R filters show
some scruff in RA.
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RR Lyrae Stars, Horace A. Smith, 1995, Cambridge
Astrophysics Series
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RR Lyr c and RR Lyr ab population distributions
in M3 and M15
http//iopscience.iop.org/1538-4357/530/1/L41/pdf/
995789.web.pdf
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But where are these two different populations?
And can Period/Luminosity flux density
distributions help determine the core from outer
regions?
Stanek video of 12 images in one night (4 of
each, Red, Green and Blue filters), 1998 on the
1.2 m. telescope at F.L. Whipple Observatory in
Arizona. https//www.cfa.harvard.edu/jhartman/M3
_movies.html
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We can make period/luminosity plots of VPHOT
data. This is one night of data for 243 Stetson
stars and 44 K28 images. But how do we find the
two populations and their period/luminosities?
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Here are 4 nights of M15 K28 images, which do
show a positive slope for the aggregate light
curves for different filter magnitudes (g r) in
this case, but then the residuals show something
else.
R code from Grant Fosters book Analyzing Light
Curves A practical Guide, 2010, Lulu Press
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Can amateur astronomers understand all this?

• Photo from home page of Natalia Dziourkevitch
  http//www.aip.de/nsd

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How about just enjoying the show. And keep the
camera focused!
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Core Period/Luminosity

• Not sure I'm saying this right, but it would be
  something like this there is a P/L ratio
  differences between core and outer region, which
  would be a Bayesian prior, which would inform
  the decision to describe the core region. For
  example  when the core's P/L ratio is negative
  at some slope, large enough to be significant
  when compared to the positive P/L ratio slope for
  the outer region's RR Lyr stars, then this
  difference in slope of the P/L ratio would help
  inform the algorithm used to describe the core,
  and we could be confident we've identified the
  core, in-part because of the difference in the
  slope of the P/L ratios?
• That way whether or not we use some B - V color
  relationship to define the P/L ratio, or a flux
  density period/luminosity ratio over time
  (multiple images), we could still determine a
  significant change of the P/L slopes between
  core and outer region?  Such that, where there is
  a 'significant' change in these slopes, which
  identifies the core.This all depends on the
  idea that the P/L ratio of the core RR Lyr stars
  is less than the P/L ratio of the outer region's
  RR Lyr stars.
• Jamie Riggs