Another Short Post

Hi everyone! Again, not a lot to say this time 'round. After finishing by-hand image subtraction Dr. Milne and I decided to have a go with ISIS and see if our goddess of magic could do a better job than us. As it turns out, she can't, so for the time being image subtraction is a thing of the past. We currently have completed two sets of data that have been submitted to two different teams publishing papers, and have finished the work we set out to do at the initiation of the project. Right now, we are still looking into more ways we could model the light echo around SN2007af so we can update our modeling scripts (which are written in perl and plotted with IDL). As more work is done there I'll hopefully be able to post more in-depth stuff about what we're doing. In the meantime, though, thanks so much for reading!

An Update in Brief

Hi everyone! I don't have much new to say right now, unfortunately - recent weeks have seen the continuation of more work on image subtraction, which seems to be an amorphous, multi-headed beast, growing two new heads each time an old one is severed, eternal, and ever-growing. All that aside, though, I recently finished work on analyzing 2009ig, and we're preparing to move onto a newer, brighter supernova -this one recent enough that observations this year can still yield results, which means I may get to go observing soon! In addition, after preliminary work is finished on the newer candidate, we plan to return to an older candidate that has shown anomalies in dust color. The dust seems to be much bluer than Milky Way dust, and we'd love to be able to find a way to explain that. Besides that, I don't have much new to announce. Thanks again, all!

Let's be Negative (sometimes): Image Subtraction (Week 5)

This week, I decided to continue (sort of) last week's post about technology - I will be going through a routine I wrote for image subtraction line-by-line and explaining the process, hopefully elucidating more about how IRAF works.


Essentially, image subtraction is exactly what it sounds like - we take one image and subtract another one from it. More exactly, the value of each pixel in the subtrahend is removed from the value of each pixel in the minuend (so subtracted images need to have the same amount of pixels). Image subtraction can allow us to see changes in an image. Below is a sample routine for performing image subtraction in IRAF.

Lines 1 and 2 open the necessary packages in IRAF to execute the rest of the code. The "images" package contains a lot of functionality for manipulating images, including the "imgeom" package which houses image geometry packages and routines. In line 4, we start by removing any subtrahend images that might have existed beforehand - running this code is usually an iterative process, with small changes being made to both the science and subtraction images. big_09igB_sub.fits is the name I gave to the subtraction image for images from the Bigelow telescope in the B filter of SN2009ig, while bok_09ig_sub.fits is the name for the subtraction image for Bok images in the B filter. We need two files because the Bigelow and Bok CCDs have different sizes, resulting in different image dimensions.

Line 5 magnifies our original image of the galaxy before the supernova (here UGC_02124:I:B:d1996.fits) by a factor of 0.734 in each dimension (the x and the y) and spits out the image big_09ig_sub.fits.

A portion of UGC_02124:I:B:d1996.fits. The full image is longer in the x direction.

The number 0.734 in the magnification factor is determined by examining the science image and the above image to determine which is bigger. Line 7 removes all images that start with "temp1" and have a capital "B" just before the .fits extension, because these images will be created in the next step. IRAF cannot overwrite images. Line 8 rotates the image big_09ig_sub.fits through 0.4 radians and spits out the image temp1_big_100224_09igB.fits. The 100224 refers to the date; 10 is 2010, 02 is February, 24 is 24. This specific rotated image will be used to subtract the science image from February 24th, 2010, shown below.

This file is 100224_09igB.fits. The supernova lives in the green circle, which does not exist in real life.

Line 10 removes all images of the form sci*B.fits, because again IRAF cannot overwrite images. In line 11, we copy a region (375 to 775 in the x, 486 to 766 in the y) of the original science image (100224_09igB.fits) and write the file sci_100224_09igB.fits, so if we make a mistake we still have the original around. The region we choose depends on the object; in the case of a supernova, it is usually convenient to leave just the area around the host galaxy, which is what we chose to do here. In line 12, we copy the region [400:800,2:282] of the rotated subtraction image temp1_big_100224_09igB.fits and spit out the file temp1b_big_100224_09igB.fits. The region we choose here has to result in an image that matches exactly the dimensions of the science image we are going to subtract from. It also has to include the same objects otherwise the exercise is pointless.

The block of code between lines 15 and 17 first removes images that would be overwritten, and then convolves our subtraction image temp1b_big_100224_09igB.fits to a Gaussian fit with a sigma of 1.2 (you can think of this as blurring the image by a factor of 1.2) and outputs a temp2 file. The next line multiplies the value of every pixel in the temp2 image by 1.15 and gives us our temp3 file.

The final block of code is where the actual subtraction takes place. First, we remove image files that would be overwritten and the special sh.db file ("shifts database" or something like that). The xregister command we call into effect takes our two images and registers them around a region of our choosing, with the goal of matching up the position of their pixels exactly. The box we want to align them around is [250:420,180:320]. xregister outputs a shifts database file that tells us what the shift between the images is, and also the image xr_100224_09igB.fits, which we finally subtract from sci_100224_09igB.fits to obtain the final subtracted image final_big_100224_09igB.fits displayed below.

The supernova is the obvious white dot. The blackish part is where the galaxy was slightly oversubtracted due to saturation issues with the CCD, and a star that doesn't quite match up is seen to the left.

The code then logs out of the IRAF session. We run the code from a terminal with the command cl < do_imsub_B.cl (the name of the file).

The final image allows us to perform photometry of the supernova on a flat field, giving us a better and more accurate idea of how bright the supernova is alone. Were we to perform science on the original image, we would almost certainly have galaxy light contaminating our data. This image subtraction must be repeated for every image in every filter on every night of observation, and all of the boxes, shifts, multiplications, Gaussians, and rotations are confirmed by hand. Apparently there exists a software called ISIS (short for Image Subtraction Sofware, somehow, and named for the Egyptian goddess of magic) that can do it all automatically.

Magic indeed. No need to look so smug, Isis.

ISIS, unfortunately, is somewhat of a black box. You put in two images and you get one out without knowing exactly what happened inside. For that reason, Dr. Milne and I choose to go through and do it by hand. If for some reason we aren't able to get satisfactory results, we can always plug our data into ISIS and get (hopefully) better results. For now, though, my time is dominated by doing image subtraction.

That's all I have for this week, lovely readers. Until next time!

We Have the Technology: Week 4

Welcome back, everyone! This week's post is going to be a bit shorter than previous weeks. Primarily, I plan to explain the technology and instruments that we have used in the gathering, reduction, and analysis of the supernova data we have. Some of what I actually do in the process will be explained.

A logical place to start would be with the telescopes that gather most of our data. Because Dr. Milne lives here in Tucson, most of our data comes from telescopes in the area. Dr. Milne most often receives observing time on Mt. Bigelow and Kitt Peak. The supernova data obtained from Mt. Bigelow comes from the 61-inch Kuiper telescope. The Kuiper is quite old, and was originally used to scope out a proper spot for the '69 moon landing, among other lunar missions. It's currently owned and operated by Steward Observatory, and is generally used for observing by astronomers from the 3 Arizona State schools (U of A, NAU, ASU).

The 61" Kuiper telescope. Courtesy Steward Observatory.

The Kuiper is equipped with the Mont4K CCD, which can take data in the Bessel-U, Harris-B, Harris-V, Harris-R, and Arizona-I filters. The filters correspond roughly as follows: U-ultraviolet, B-blue, V-green (visible), R-red, and I-infrared (near-infrared). About half our data has come from the Kuiper.

Much of the rest of our data was gathered on Kitt Peak, at the 90" (2.3m) Bok telescope. The Bok is the largest telescope owned solely by Steward Observatory, and was dedicated in 1969. In 1996 it was named in honor of then Steward Observatory head Professor Bart Bok.

The Bok 90" telescope. Courtesy Wikimedia Commons.

The Bok telescope has instruments that allow for both imaging and spectroscopy. The Bok telescope mainly uses 3 instruments; the 90prime, which does visual-range imaging, the B&C Spectrograph, which does visual spectroscopy, and the Steward 256x256 NIR camera, for infrared observations. Our data comes primarily from the 90prime instrument, although in future observing runs we hope to obtain some spectroscopy data for a relatively recent light-echo candidate supernova. Most of the other half of our data has originated from the Bok telescope.

We have a small amount of data from the Large Binocular Telescope, or LBT, on Mt. Graham. The LBT is one of the world's most advanced optical telescopes, making use of two 27-foot mirrors which together give it the light gathering capability of a single 39-foot mirror and the optical clarity of a 75-foot mirror.

The Large Binocular Telescope. Courtesy Wikimedia Commons.

Although not very much of our data has originated from the LBT due to considerable difficulty in getting observing time on the telescope, the data we do have from there are of unusually high quality.

The last of our data has come from the Holy Grail of telescopes, the Hubble. The data were not, in fact, taken by Dr. Milne but rather in a number of surveys conducted primarily by Nobel Laureate Dr. Adam Riess in searching for cepheids in other galaxies to get a better understanding of the expansion rate of the universe. A few data points are from the HST images, while the other images were primarily used in subtraction.

I have been observing with Dr. Milne at both the Kuiper and Bok telescopes, though our observing targets were not the supernovae that my research focuses on.

In addition to giving an overview of these telescopes, I would also like to briefly introduce the software that Dr. Milne and I have been using for image analysis. It's called IRAF (image reduction and analysis facility), and is a collection of many software components written by the National Optical Astronomy Observatory (NOAO). There are many packages and tasks that IRAF can perform. My roles primarily include fixing bad pixel strips, combining raw data images into stacked, usable data, performing subtraction on images to remove the background field from the supernovae, obtaining useful information about how bright objects are, and plotting the results. Each step involves quite a bit of code and user input, so this analysis is very time consuming. The results, however, tell us all of the information about the light echo I've mentioned previously; brightness, angular size, distance, color, and all the rest. In the past week, I have primarily been focused on stacking the raw images of our 2009 supernova, with some effort being put into subtraction on these same images.

That's all I have for you this week. I hope it wasn't too boring! Thanks for reading, everyone, and tune in next week for another post.

The Geometry of Light Echoes and Week 3 Updates

Welcome back, everyone! This week, I would like to do a brief overview of the geometry of the kind of light echo described in the previous post. Buckle up for some math (though not too much)!

Light Echo Geometry

So, the biggest question is how we get meaningful information from a light echo that we have detected. In some cases, it's not necessarily possible, but if an image of the light echo is taken that has sufficient angular resolution to make out the ring, a wealth of information can be obtained. Take a light echo that is observed to have a radius of x pixels.

Not to scale.

Our first task is to find out what x is in some unit of distance in physical space. To accomplish this, we need to know what's called the plate scale of the image - the plate scale tells us the angular size of each pixel in the sky. For example, in the Hubble instrument used to observe our supernova, the plate scale is 0.04 arcseconds per pixel (where 1 arcsecond is 1/3600 of 1 degree). The plate scale tells us the total angular size of the light echo's radius (say, θ). In order to translate this angle into a physical size, we need to know the distance to the supernova's host galaxy (call it D). Using trigonometry, we find the physical size ρ of the light echo to be ρ=D tanθ. Now that we have an idea of the physical size of the light echo, we can use the geometry of the ellipsoid to determine the distance from the supernova explosion to the dust causing the echo. It is a well-known result that

F. Patat, Reflections on Reflexions (2005)

where t is the time elapsed between the supernova being at peak magnitude and the measurement being taken. Using this and our previous relation, we find through routine algebra that the distance z between the supernova and the dust is

This tells us how far away the dust is from the supernova, and thus gives us an idea of what the progenitor system might have been like before the explosion. This also tells us what must happen to a light echo as time passes; in order for z to remain constant as t increases, the quantity tanθ must necessarily increase, which implies that the size of the echo must increase. The ring will become larger as time passes.

If there are multiple dust sheets between the supernova and us, all at different distances, it is possible that light will echo off of each one, resulting in a properly timed image showing a series of concentric rings around the location of the original supernova. Such is the case with famous supernova SN 1987A, one of the best-known examples of a supernova with a light echo.

Anglo-Australian  Telescope photograph by David Malin

It is typically assumed that the progenitor systems of type Ia supernovae are not particularly dusty (i.e., that the dust typically responsible for a light echo is interstellar, and quite far away from the supernova). To show that this is not true would be an interesting insight into how these remarkable phenomena come about.

In some cases, the light echo as imaged is not a ring. In such cases, similar analysis as above can be performed making the same assumption of a sheet in front with allowances made for blurring in imaging or insufficient angular resolution to resolve a ring. Another possibility is that of dust being either behind or in the area immediately surrounding the supernova. If instead of the light rebounding to us off of a sheet of dust in the foreground it gets to us because it rebounds off of a dusty medium in which the supernova is immersed, it may appear as a solid disk rather than a ring when imaged. Through detailed analysis using the image reduction software IRAF, Dr. Milne and I plan to explore the possibility of such circumstellar material around light echoes for which we have data.

Week 3 Updates

In my internship, I have primarily continued to refine the computer simulations of our light echoes. Written in perl, the simulations allow us to compare different models of dust distribution to actual data, (hopefully) allowing us to figure out which one best fits real life. In addition, I have begun to stack more data of our supernovae with the goal of producing a more accurate light curve that can be included in a collaborator's paper. I have also continued my reading of papers and books concerned with both Type Ia supernovae and light echoes. Some of the math is still beyond my reach (some flux calculations in Reflections on Reflexions, for example), but it's definitely coming along!

What Is a Light Echo?

Hello again everyone! Now that I've defined what a type Ia supernova is, I think it would be appropriate to define what a light echo is. This should be a shorter post than the last one. Before we start, I'd like to mention the naming scheme for supernovae. It is fairly simple; they are named by the year they are detected. The first supernova in 2015 will be SN 2015A. The second, SN 2015B and so on. After SN 2015Z, we get SN 2015AA, SN 2015AB, and so on. No distinction is made between supernovae types with this naming scheme.

Light Echoes

As mentioned in my previous post, type Ia supernovae are critical to modern cosmology, and a full understanding of how exactly they come about (i.e., the progenitor systems they arise from) is not currently at hand. Due to their importance, such an understanding is desirable. Analyzing a light echo is one possible method of probing the environment of a supernova's progenitor system.

Based on a diagram by Armin Rest, Harvard University

Above is a diagram of a light echo. Light from the supernova is directed radially outwards, and some of it is directly headed towards Earth (represented as a red arrow on the diagram). This light will reach us first. However, some light that would not initially have been visible from Earth can scatter o ff of interstellar dust (in the diagram, the light blue band is a sheet of interstellar dust) and redirect itself towards us (represented by the blue arrows on the diagram). The longer path length this light travels necessitates that it arrive at Earth at a later time, much as an echo arrives at a later time than the original sound. Surfaces of constant arrival time are traced out by an ellipsoid, which in most cases can be approximated as a paraboloid because the distance between the observer and the supernova is very large (an ellipsoid with one focus approaching infinity). If the dust that scatters the light is a sheet between the supernova and the observer, the echo will take on the appearance of a ring of light around the original supernova. The positioning and size of this ring can be used to discover the distribution of dust around the progenitor system, and thus discern some properties of the progenitor system that would not otherwise be known.

A light echo around V838 Monocerotis. The echo is the brown ring. Courtesy Wikimedia Commons.

Oftentimes telescopes that observe supernova lack the optical resolution to see an actual ring around a light echo. Therefore, we must usually rely on other methods to detect the presence of a light echo. Type Ia supernovae have characteristic ways in which their light fades off. Most commonly, such a fading is shown through a light curve, which plots some measure of luminosity or magnitude versus time.

An example of the light curve of a type Ia supernova. The capital B is the filter. R. Cadonau, 1987.

Because the light that scatters off of the dust arrives at later times, it will often arrive as the supernova itself is fading. This is shown in the light curve as a flattening, as light from the echo overcomes the light from the fading supernova. So, if you have a type Ia supernova with a light curve that flattens out, you might have a light echo on your hands. This is the most common method of detecting light echoes.

Supernovae in General, and Week 1 Updates

While my internship is starting up, I think it might be a good idea to get a few terms out there so the rest of the blog makes sense! The first of these is "supernova".

What Is a Supernova?

In general, the term "supernova" (abbreviated SN) refers to a star exploding. Not all stars do this, but when they do, it's big. Supernova explosions (supernovae, or SNe) are some of the most energetic phenomena in the observable universe. If a supernova were to occur where the sun is now, the amount of radiation and energy your face would receive from looking at it would exceed the amount from a typical nuclear bomb exploding while touching your nose. Stars that go supernova briefly rival the brightness of their host galaxies, expending all their energy in a final violent display. The material left behind in a supernova contains heavier elements than iron, because the high amount of energy present in the explosion is enough to trigger fusion of heavy elements. All elements heavier than nickel were created by supernovae phenomena (except laboratory elements, of course). Supernova remnants (the remains of these violent explosions) are some of the most beautiful visible-light objects in the sky.

The crab nebula, a supernova remnant. Courtesy Wikimedia Commons.

The most well-known kind of supernovae in the public eye are type II supernovae, or core-collapse supernovae. These supernovae occur in very massive stars, between 8 and 50 solar masses. Because of their large mass, these stars can continue the fusion chain past hydrogen and helium, fusing elements in concentric layers until eventually reaching a point where they fuse their cores into iron or nickel.

The onion-like layers of a star about to go supernova. Courtesy Wikimedia Commons.

Fusing iron and nickel provides no net energy output, so pressure from the core is lost and equilibrium is broken. The star is held up through only electron degeneracy pressure. When the mass of the core exceeds the Chandrasekhar limit of about 1.4 solar masses, electron degeneracy pressure gives way to gravity and a catastrophic implosion occurs. The outer core of the star reaches velocities of up to 20% the speed of light, while the inner core reaches temperatures in excess of 100 billion Kelvin. Eventually the star collapses far enough for neutron degeneracy pressure to come into play, and the collapse rebounds and explodes outwards. The core of the star is left behind as either a neutron star (if the star is less than 20 solar masses) or a black hole (if the star is more than 20 solar masses). A neutron star is composed almost entirely of neutrons held up by neutron degeneracy pressure, while a black hole is a singularity.

Although they are interesting, my research does not focus on type II supernovae (as the title of the blog may have hinted). Instead, I'm focusing on the slightly less popularized (but no less interesting!) type Ia supernovae. In general, type I supernovae occur from stars called white dwarfs. When stars on the so-called main sequence (stars like our sun) get very old, they expand to enormous stars called "red giants" before fluffing off their outer layers, leaving behind a tiny, dense ball of electron-degenerate matter called a "white dwarf" (because it is small and white).

The Sirius star system, containing a white dwarf, the faint dot below and to the left of the main star.

White dwarfs do not undergo fusion, and emit radiation because they are hot. Usually, these white dwarfs will simply live out their lives in relative peace, and are expected to eventually cool until they are no longer energetic enough to emit light or heat (becoming so-called "black dwarfs"). Some, however, are destined for a more exciting fate. However, if the white dwarf is in a binary system with another star (like in the above photograph), it's possible for it to end its life in a more spectacular manner. It can pull (or "accrete") mass from its companion star, and if enough mass is gained it will exceed the Chandrasekhar mass (1.44 solar masses, different than the Chandrasekhar limit mentioned above) and they will begin a runaway fusion reaction. Enough energy is released for the star to explode violently in a type Ia supernova.

Type Ia supernovae are particularly important to cosmology because of their uniform nature. They reach a consistent peak luminosity because of the uniformity of the white dwarf progenitor systems. This makes them ideal candidates for so-called "standard candles" that can be used to determine the distances to other galaxies. If a type Ia supernova goes off in NGC 5584, for example, we know what we observe to be it's peak magnitude (or its apparent magnitude), and what its actual (or absolute) magnitude should be, allowing us to calculate the distance to NGC 5584. Such calculations give critical information about the expansion of the universe, making type Ia supernovae critical to the study of the evolution of the universe.

Although type Ia supernovae are very important to modern astronomy, surprisingly little is known for certain about how they come about. The above model of accretion is called the "single degenerate" progenitor model, because it only contains one degenerate star (the white dwarf). Other models such as the double degenerate model propose that two white dwarfs can collide and produce a supernova explosion. Probing the progenitor systems of type Ia supernovae is important in determining how these remarkable events occur.

Internship: Week 1

The first week of my internship has been afflicted with a horrible disease known as "technical difficulty." Data transfer between computers, installing new operating systems, getting licensing for all of the software working, and finding out we don't have all the data we thought we had have all been problems encountered thus far. Despite these setbacks, much work has been done and much progress made. I have done considerable reading from the theses of two of Dr. Milne's graduate students, Dina Drozdov and Ginger Bryngelson, and read through several papers on previous light echoes in type Ia supernovae. Additionally, I have done work on refining and improving the computer simulations of the light echo in our 2007 supernova, with the goal of better understanding the geometry of dust around the progenitor system.