Copyright © Michael Richmond.
This work is licensed under a Creative Commons License.
The next technique is a little bit like TRGB, because it
Instead of looking only at the very brightest red giants, however, this method includes all the bright red giants in a galaxy, together.
Back in the Old Days, newspapers were created using relatively simple (in some ways) printers. Many had just a single color of ink -- black -- and could not apply layers with different thickness or intensity. Each bit of paper would be covered with a spot of black, or left perfectly white. Nothing in between.
And yet, despite this on-or-off, black-or-white only technology, newspapers were still able to display drawings and photographs that presented a more realistic view of the world:
Image taken from
"Halftone", by Dusan C. Stulik and Art Kaplan,
courtesy of
The Getty Institute
Q: How did newspapers produce such subtly shaded portraits
using only pure black and pure white?
Need a clue? Consider this small portion of the picture.
Image taken from
"Halftone", by Dusan C. Stulik and Art Kaplan,
courtesy of
The Getty Institute
If we magnify this region, we can see that it is actually composed of little dots of black ink on a pure white background.
Image taken from
"Halftone", by Dusan C. Stulik and Art Kaplan,
courtesy of
The Getty Institute
When our eyes are confronted with a mass of tiny little dots below the limits of their resolution, the dots begin to blend together to form shades of grey. When viewed without any magnification, at an ordinary distance, the picture appears to show smooth gradations of intensity.
We might summarize the effects of halftone printing like so:
If you understand this change in appearance as a function of distance, you'll understand the method behind Surface Brightness Fluctuations, too!
Let's consider a simple situation: a one-dimensional "galaxy" made up of bar-shaped "stars". If the galaxy is close enough, we can resolve the individual "stars", so that each one is separated from its neighbors by empty, black space.
Note the high contrast
If the galaxy is ten times farther away, then the stars begin to blend together. The average pixel now contains light from one star (appearing light grey), but due to the random location of stars, a few pixels are still empty (black), and a few pixels contain the combined light of several stars (bright white).
No longer pure black vs. pure white
If we move a single galaxy farther and farther away, the average pixel contains a blend of light due to a larger and larger number of stars; as a result, the range of pixel values decreases, since the size of the random fluctuations decreases as we add together more and more stars. In the figure below, the gold bars show how the entire image at 1 Mpc is compressed into the first 10 pixels of the image at 10 Mpc, the entire image at 10 Mpc is compressed into the first 10 pixels of the image at 100 Mpc, and so forth.
The pattern is clear:
Let's quantify these statements. In the synthetic one-dimensional "galaxies", there is an average of 1 star for every 10 pixels when viewed from 1 Mpc. If every star has an identical intensity of 1 unit, then the average pixel value must be 0.1.
When we view this "galaxy" from a distance of 10 Mpc, each pixel now contains 10 times as many stars. I've scaled the intensities so that the average value is still 0.1, but you can see that the changes from one pixel to the next are now much smaller. If you click on the picture, you'll see the progression as we move the galaxy from 1 Mpc to 10000 Mpc.
We can be even more quantitative by computing the fractional difference from the average pixel value, on a pixel-by-pixel basis. If a galaxy is close to us, this fractional difference can be very large, but it shrinks rapidly with distance.
As one might expect, there's a simple relationship between the distance of the galaxy and the typical size of these deviations from the average pixel value.
One could use this relationship to determine distances in the following way:
Now, in the real world, with its three-dimensional galaxies consisting of billions of stars drawn from heterogeneous populations, the problem is much more complicated; but the basic idea is the same.
Let's look at a real example, taken from Blakeslee, Ap&SS 341, 179 (2012). HST observations of the galaxy IC 3032 in the Virgo Cluster show a pretty typical elliptical: bright at the center, fading away at larger distances:
Taken from Fig 7 of
Blakeslee, Ap&SS 341, 179 (2012).
If one makes a model of the galaxy's brightness, fits it to the distribution of light in the image, and subtracts it from the original, one is left with ... lumps. (Click on the image to activate animation)
Adapted from Fig 7 of
Blakeslee, Ap&SS 341, 179 (2012).
Those lumps are NOT individual stars in the galaxy; for one thing, they are much brighter than even the brightest red giants at this distance. Instead, they are due to Surface Brightness Fluctuations (SBF) in the number of bright giant stars falling within each resolution element of the image.
One way to measure quantitatively the size of the fluctuations in a galaxy's light is to take the Fourier transform of the two-dimensional image of the residuals, after the smooth model of galaxy light has been subtracted. If the galaxy is nearby, then the power of those fluctuations (the amplitude of the curved line in the diagram below) will be large:
Figure taken from
Tonry and Schneider, AJ 96, 807 (1988).
If the galaxy is distant, then the power of those fluctuations will be small:
Figure taken from
Tonry and Schneider, AJ 96, 807 (1988).
Now, real life is much more complicated than that simple example.
So the basic ASSUMPTION that the stellar census in old populations of all galaxies is identical has to be modified. Astronomers who use the SBF method must try to account for variations in the population of stars from one galaxy to the next. It's a very complicated business.
The literature on SBF often uses the notion of the "fluctuation magnitude", denoted by a magnitude with a horizontal bar over it. This "flucuation magnitude" depends on the mix of stars within the overall stellar population; but in many cases, it is dominated by the light of giant stars. It is, alas, not exactly the same in all galaxies, because the stellar population isn't the same in all galaxies. Fortunately, it doesn't very VERY much if one chooses a set of galaxies with similar properties, so as long as one compares, say, giant ellipticals to giant ellipticals with similar colors, the method is pretty reliable. Look at these results for two sets of galaxies in the Virgo and Fornax clusters:
Figure taken from
Blakeslee et al., ApJ 694, 556 (2009)
Q: What is the difference in distance modulus between
Fornax and Virgo, using these SBF measurements?
Is this value reliable? Well, one way to find out is to measure the difference in distance modulus using some other technique, and see whether the two methods agree or disagree.
You may recall that the TRGB method suggested that the distance modulus to NGC 1365 in the Fornax cluster was (m-M)Fornax = 31.29. Another study using TRGB
finds that the distance modulus to the Virgo Cluster is (m-M)Virgo = 31.05.
Q: What is the difference in distance modulus between
Fornax and Virgo, using the TRGB method?
Q: Do the TRGB and SBF methods agree, or not?
The SBF method appears to give relatively precise distances when used properly; Blakeslee et al., ApJ 694, 556 (2009) claim an intrinsic scatter of only about 0.06 mag. We can check this by looking at a recent determination of the distances to galaxies in the Fornax cluster.
Figure 4 taken from
Blakeslee, J. P, ApSS 341, 179 (2012)
This method works best at long wavelengths, in the optical I-band and in the near-infrared, because emission from a galaxy at those wavelengths is dominated by a relatively few, luminous, red giant stars. If we observe at shorter wavelengths, then we dilute the light of these few, luminous giants with the light from many more less-luminous subgiants and main-sequence stars. That means that the number of stars contributing to the light inside each pixel (or resolution element) increases, and the size of random fluctuations in that light will decrease.
Two reasons the SBF method is so promising are
The reach of the SBF method is larger than that of other methods we have examined so far. It appears that SBF can be used to measure distances to the Coma Cluster of galaxies -- which it finds to be about 95 Mpc away from us, roughly six times more distant the the main Virgo Cluster!
First, a near-IR image of the galaxy NGC 4874 taken with HST at 1.6 microns (in H-band):
Taken from
Jensen et al., "The Surface Brightness Fluctuation Distance to the Coma Cluster" (2015)
Now, the same image after subtracting a model for the galaxy's light, leaving surface brightness fluctuations and a boatload of globular clusters.
Taken from
Jensen et al., "The Surface Brightness Fluctuation Distance to the Coma Cluster" (2015)
So, we can now measure the distance to the Coma Cluster (and other objects at similar distances) via SBF.
Do different methods yield the same result? Consider the galaxy NGC 3379.
Q: What is the distance to this galaxy, based on TRGB?
(make a color-magnitude diagram from the data in the file above
and assume the absolute magnitude in I-band is M(I) = -4)
Q: Has anyone measured the distance to this galaxy via the SBF
technique? If so, provide a reference to the paper
and the distance.
Q: Do the two methods agree?
Copyright © Michael Richmond.
This work is licensed under a Creative Commons License.