Luminosity Functions of Planetary Nebulae & Globular Clusters By Azmain Nisak ASTR 8400
Calculating Distance! m = apparent magnitude! M = absolute magnitude! r = distance in pc
GLOBULAR CLUSTERS AS DISTANCE INDICATORS
GCLF: Procedure! Collect apparent magnitudes of as many globular clusters as you can.! Plot these in a histogram. This magnitude distribution is called the Globular Cluster Luminosity Function (GCLF).! Fit this function to some standard law! The apparent magnitude corresponding to the peak of this distribution is called the Turn-Over Magnitude (TOM)! It is known that the absolute TOM is a constant (M V,TO -7.5)! Use the distance modulus equation to solve for distance
GCLF: Example
Why GCLF! Comparison of TOMs for galaxies at the same distance (i.e. same galaxy cluster) reveals a scatter of 0.15 without correcting for any error! Taking into account errors, internal dispersion of TOMs is <0.1, which makes globular clusters a useful standard candle! A constant absolute TOM suggests a universal characteristic mass in the globular cluster mass distributions in all galaxies. The origin of this is still unclear! Distance over which GCLF can be used is constrained by limiting magnitude required to reach the peak of the GCLF Using Hubble Space Telescope (HST) or 10-m telescope, reaching V ~ 28, the method can be applied up to 120 Mpc (including Coma galaxy cluster)! Globular clusters are brighter than other standard candles (except for supernovae), do not vary (i.e. no repeated observations), and are usually measured at large radii or in the halo of (mostly elliptical) galaxies where reddening is not a concern.
Fitting the GCLF! Which standard law is used? Gaussian t5 function
Gaussian vs. t5! Left: Milky Way GCLF fitted with a Gaussian (solid line) and t5 function (dashed line) in magnitude units! Right: Milky Way GCLF fitted with a Gaussian (solid line) and t5 function (dashed line) in luminosity units! t5 fits better overall but both are sufficient to getting the TOM
Example Calculation! Kavelaars et al. (1997) confirmed the TOM for NGC 4697, a calibrator galaxy of the Virgo cluster. They calculated m R TO = 22.9, m-m = 31.0, and V-R = 0.6. What was the M V TO they calculated?! M V TO = -7.5
Sources of Error! Must correct for luminosity function of background galaxies (these tend to mimic a fainter TOM! Must account for photon noise as a function of galactocentric distance, which can affect how incomplete your sample of GC is! Must apply correction for reddening. The correction you make depends on what reddening map you use! In some images, the clusters may be slightly extended. Therefore, a proper aperture correction must be applied.! The function you use to fit your GCLF can have an effect on your computed TOM. The most commonly used functions are Gaussian and t5! What you consider the absolute TOM depends on what globular cluster system (GCS) you are calibrating with. This can introduce some error! Your GCLF may be impacted by galaxy type due to mean metallicity of globular clusters differing in early- and late-type galaxies! The net effect of these errors sum up to several tenths of a magnitude]
Two Main Methods! Classical Way Uses all globular clusters in a galaxy Uses GCLF as a secondary distance indicator, calibrating to elliptical galaxies in the Virgo cluster, whose TOMs are determined from primary distance indicators (like Cepheids)! Alternate Way Uses metal-poor globular clusters only Uses GCLF as an independent distance indicator, and uses the Milky Way GCLF for calibration. The Milky Way GCLF is determined by calculating distances to globular clusters in the Milky Way using the known apparent magnitudes of their horizontal branches and a relation between the absolute magnitude of the horizontal branch and the metallicity. (see Gratton et al. 1997 for more details)
The Classical Way! Advantages Using all globular clusters in a galaxy as opposed to a limited sub-population avoids problems with small number statistics. Using Virgo GCLFs instead of the Milky Way GCLF is useful because these are giant elliptical galaxies rich in globular clusters, are well-sampled, and do not suffer from small number statistics.! Disadvantages Giant ellipticals are known to have globular cluster subpopulations with different ages and metallicities. Therefore, using all globular clusters in the galaxy causes one to sample a mix of TOMs. This causes the GCLF to become broader and its TOM to be displaced. Errors of several tenths of a magnitude are introduced. Using GCLF as a secondary distance indicator is problematic because errors from the primary distance indicators used for calibration carry through.
The Alternate Way! Advantages Takes into account subpopulations in Globular Cluster Systems (GCS).! We use metal-poor globular clusters (GC) because they appear to have a true universal origin, their properties are relatively independent of galaxy type, environment, size, and metallicity, they appear to be halo objects weakly affected by those GCs closer to the galactic center or those on radial orbits, and because they will form a much more homogenous population than the total GCS. The Milky Way GCLS is a good calibrator because its GCLF is independent of other distance indicators (like Cepheids).! Disadvantages Choosing metal-poor globular clusters requires more complicated and timeconsuming observations Perfect separation is not possible and there will probably always be some contamination of metal-rich clusters. The sample size will be cut in half, inducing errors > 0.1 on the GCS TOM.
Recent Result! Rejkuba, M. (2012) reveals Left: Milky Way GCLF using all GCS (Black) vs. metal-poor GCS (Blue) Right: Dependence of TOM on metallicity and filter for Milky Way GCS
PLANETARY NEBULAE AS DISTANCE INDICATORS
PNLF: Procedure! Identify as many planetary nebulae in the galaxy of interest as possible, making use of their bright [O III] λ5007 emission line.! Make a histogram of the apparent magnitudes of these objects at this wavelength. This distribution of magnitudes is called the Planetary Nebula Luminosity Function (PNLF)! Fitting the distribution to a standard law, identify the magnitude of the brightest planetary nebula in the galaxy! Calibrating to the known absolute magnitude of the brightest planetary nebula, use the distance modulus equation to compute the distance to the galaxy.
Why PNLF! One of the most reliable ways of getting distances to elliptical galaxies out to about 20 Mpc. The limiting distance for this method may be 50 Mpc for an 8-m telescope with excellent detector and seeing! Good agreement with other distance indicators Disagreements between PNLF and other reliable methods (i.e. Cepheids) are smaller than 8%. Thus, systematic errors due to extinction, age, metallicity, or application of the method are not accumulating beyond the 8% level. In fact, if errors from Cepheid distances are taken into account, the PNLF errors must be smaller than ~ 5%.! PNLF is insensitive to population age and metallicity! PNLF is invariant with Galaxy color, metallicity, and Hubble type Well defined PNLFs currently (1992) exist for 17 giant spiral, elliptical, and irregular galaxies. In none of these objects is there any evidence for a change in the shape of the PNLF cutoff! M = 4.47 ± 0.05
Fitting the PNLF! Truncated exponential is most popular:
Problems and Sources of Error! Contamination H II Regions: Star formation is not an issue in most elliptical and lenticular galaxies, but in late-type systems, the H II regions around O and B stars will far outnumber the PNe. Fortunately, most H II regions are resolvable under good seeing conditions, and their exciting stars may be visible on deep continuum images. Supernova Remnants: Unresolved high-excitation supernova remnants can masquerade as planetary nebulae, especially in galaxies that have a cold, high density interstellar medium. Because compact supernova remnants are rare, their effect on the PNLF is minimal. Lyα Galaxies: At z = 3.12, Lyα is redshifted to 5007 A. Unresolved and marginally resolved high-redshift galaxies with extremely strong Lyα emission can mimic planetary nebulae. The surface density of these star-bursting objects is relatively low so PN surveys in galaxies are not strongly affected by this contaminant.
Problems (cont.)! Correcting for interstellar extinction Must correct for extinction in Milky Way. Can use reddening maps. Internal extinction in host galaxy (only a problem in late-type spiral and irregular galaxies). Estimated to be approximately equal to or greater than 0.5 mag.! Considerations for Spirals Potential confusion between PN and H II regions Spiral arms contain dust lanes that could reduce observed luminosities A young population of stars must exist within spiral arms
Recent Result! Mendez R. (1999) computes values for PNLF of M81 using M31 (770kpc) as calibration. Obtained m(5007) = 23.64, m-m=27.78, extinction correction of 0.36, and M = -4.54.
References! Ciardullo, R., The Planetary Nebula Luminosity Function, ESO Intl. Workshop on "Planetary Nebulae beyond the Milky Way" (2004).! Forbes, D., Globular Cluster Luminosity Functions and the Hubble Constant from WFPC2 Imaging: The Giant Elliptical NGC4365, Astron. J. 112 (3), 954-959 (1996).! Jacoby et al., The Planetary-Nebula Luminosity Function, Publ. Astron. Soc. Pac. 104: 599-662 (1992).! Jacoby G., Verifying the Planetary Nebula Luminosity Function Method, Cambridge University Press (1997).! Kavelaars, J.J. & Gladman, Brett., Probing the Shape of the Globular Cluster Luminosity Function, Proceedings of CFHT Users Meeting (1998).
References (cont.)! Kissler-Patig, M., Extragalactic Globular Cluster Systems: A New Perspective on Galaxy Formation and Evolution, Reviews in Modern Astronomy 13, 23-29 (2000).! Mendez, R., Distances from the Planetary Nebulae Luminosity Function, Astrophys. Space Sci. 237, 161-180 (1999).! Rejkuba, M., Globular cluster luminosity function as distance indicator, Astrophys. Space Sci. 341, 195-206 (2012).! Richtler, T., The Globular Cluster Luminosity Function: New Progress in Understanding an Old Distance Indicator, Lect. Notes Phys. 635, 281-305 (2003).! http://astronomy.swin.edu.au/cosmos/d/distance+modulus