Presentation on theme: "Can amateur observers discriminate the core of dense globular clusters like M3 and M15? Rodney Howe AAVSO SID Analyst Strikis Iakovos - Marios Hellenic."— Presentation transcript:
Can amateur observers discriminate the core of dense globular clusters like M3 and M15? Rodney Howe AAVSO SID Analyst Strikis Iakovos - Marios Hellenic Amateur Astronomy Association Elizabeth Observatory of Athens Ido Bareket מצפה הכוכבים ברקת במכבים Bareket observatory, Israel Stouraitis Dimitrios Hellenic Amateur Astronomy Association Galilaio Astronomical Observatory
Video of Globular Cluster M3 Large file download ~16MB Note the variable stars scattered around the cluster!
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 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. luminositiesCepheid variablesLeavitt period-luminosity relation
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 BrightnessInverse 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.
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.
Measure field RR Lyrae distances by parallax (these two images are 7 years apart!)
RR Lyrae Stars, Horace A. Smith, 1995, Cambridge Astrophysics Series
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.
(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.” How do we discriminate the core?
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 “...
Cutting up the cluster to identify period/luminosity ratios
But, which Pixel Value should we choose? Perhaps the Full Width Half Maximum (FWHM)?
FWHM is just the yellow part of the flux density.
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)
And then compare magnitude (digital number) differences between outer image regions (more dark sky) and inner regions (no dark sky)
Cut right to the core! To follow the period changes over time.
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 1+1/2 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 “...
How about treating the cluster as just one star?
Tom Krajci’s observatory for AAVSO
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 arcsec/pixel, and frame FOV = 27 x 18 arc minutes.)
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.
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) < 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 NGC NGC7078.posNGC7078.phoNGC7078.fits.gzG26_ NGC7078.posNGC7078.phoNGC7078.fits.gz
We’ll 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.
VPHOT is used to create instrumental magnitude comparisons for each of the K28 – M15 Sloan filtered images.
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) / (g+r))
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.
RR Lyrae Stars, Horace A. Smith, 1995, Cambridge Astrophysics Series
RR Lyr c and RR Lyr ab population distributions in M3 and M15
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.htmlF.L. Whipple Observatoryhttps://www.cfa.harvard.edu/~jhartman/M3_movies.html
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?
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 Foster’s book ‘Analyzing Light Curves A practical Guide’, 2010, Lulu Press
Can amateur astronomers understand all this? Photo from home page of Natalia Dziourkevitch:
How about just enjoying the show. And keep the camera focused!
“ 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 Core Period/Luminosity