Alex Moskowitz

Brown University


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ASTRONOMICAL X-RAYS AND XQC

Introduction

What is the diffuse x-ray background?

This is a picture of the night sky as your eyes can see it...
Optical Night Sky Image

...and this is a picture of the night sky if you could see X-rays.

X-ray Sky Image


Huh? Where'd the Milky Way go? And all the stars?
Unlike the visible sky, the X-ray sky is not made up of point sources in the galaxy but is largely composed of "diffuse background." This background is due to a combination of sources, and different energy X-rays come from different mechanisms. At high energies (>.75keV), most of the X-rays come from sources outside the galaxy. However, the production of low-energy X-rays is still uncertain.(1)

Possible mechanisms include:
  • Hot gas in the Milky Way
  • Supernova
  • Stellar Winds, such as solar wind charge exchange

    Methods of X-ray production
  • Bremsstrahlung
    All accelerating charged particles give off radiation. When a high-energy electron encounters a nucleus, electromagnetic forces change the path of the electron, causing it to radiate. If the energy of the electron is high enough, it emits X-rays. Bremsstrahlung's spectrum is continuous; that is, it is made up of photons of a range of different energies.

    Bremsstrahlung spectrum

    A bremsstrahlung spectrum showing the relative number of photons observed at each specific wavelength of light. Several curves are shown, corresponding to different initial energies of the impacting electron.



  • Atomic transitions ("characteristic radiation")
    If an atom is given energy, its electron will jump to a higher energy state. As the electrons decay to their initial energy states, they release photons, many of which are X-rays. The spectrum of atomic transitions is discrete; that is, X-rays are only detected at extremely specific wavelengths, which makes them easily identifiable.

    Combined Spectrum

    The spectrum of x-rays emitted from 35kV electron shot at a Molybdenum target. The bremsstrahlung and atomic transition components can be clearly separated.


  • Thermal Emission
    The thermal motion (temperature is a measure of the kinetic energy of a substance) of the atoms causes the atoms to radiate. Higher temperature objects emit more photons, and those photons are also higher in energy.

    Blackbody Spectrum Blackbody Spectrum Legend

    The relative intensities of light emitted at a certain energy for temperatures of 5000K (roughly the same temperature as the surface of the sun) and 1,000,000K (roughly the same temperature as X-ray emitting gas in the Milky Way)


  • Nuclear Decay
    When some types of radioactive nuclei decay, they release photons. While these photons are technically classified as gamma rays, they often have energies similar to X-rays produced by other processes.


  • Solar Wind Charge Exchange
    When an ion encounters a neutral atom in space, it is possible for the neutral atom to "donate" an electron to the ion. If this electron is donated into a high energy state, it will radiate X-rays as it transitions to the lower energy state. SWCX radiation is similar to characteristic radiation, although the mechanisms involved are very different--characteristic radiation involves the excitement of an electron in a single atom, whereas SWCX involves the exchange of an electron across two different atoms. Near the earth, most SWCX is between ions emitted in the solar wind of the sun and neutral atoms found in the solar system. The physics of SWCX are not yet completely understood, and this is part of the current mission for XQC.


    What is the current understanding of the source of astronomical X-rays?
    At low energies, the X-rays are primarily caused by SWCX and thermal emission of hot gas surrounding the solar system, although this hot gas contributes only about a quarter of the total X-rays. The hot gas is energized by supernova, and by the intense solar winds of young stars. At high energies, most of the X-rays are produced by sources outside of the milky way, such as quasars.



    How does XQC Work?


    XQC (the X-ray Quantum Calorimeter) is a device that uses the tiny changes in temperature caused by absorption of photons to detect X-rays. When an X-ray enters the detector, it first passes through a series of filters. Each filter blocks the wavelength of the most intense thermal emission from each different temperature stage of the detector (150K and 2K) as well as optical light. The X-ray then strikes one of the thirty-six calorimeters.

    Calorimeter Diagram

    The calorimeters used in XQC are made of three parts: the absorber, the thermistor, and the heatsink. The absorber is made from Mercury and Tellurium; the thermistor is made from silicon, and the heat sink can be made from various materials. When an X-ray hits the absorber, the electromagnetic energy of the X-ray is converted into thermal energy. This heat in the absorber flows into the thermistor, warming the thermistor. The thermistor is a resistor whose resistance changes with temperature; electronics on board XQC detect the change in voltage due to this change in resistance and use it to calculate the energy of the X-ray. In order to "reset" the thermistor, the heat in the thermistor then flows into the heat sink, which is kept at a constant temperature. Each calorimeter is half a millimeter long and two millimeters wide. In order to keep XQC's own thermal emission from drowning out the X-rays, the detector is filled with liquid helium and cooled to 50mK using an adiabatic demagnetization refrigerator (ADR). In an ADR, a magnet aligns the small magnetic dipoles of the atoms of a "salt pill"; when the magnet is turned off, thermal energy is used to randomize the magnetic dipoles.

    XQC has been launched by NASA from a Nike-Black Brant sounding rocket at the White Sands Missile Range in New Mexico. Each 15-minute flight brings XQC 220 kilometers above the earth's surface, where the atmosphere can no longer block X-rays from reaching the detector.



    Filter Transmission Models


    While the filters block thermal emission, they also block X-rays. The transmission ratio (the ratio of X-rays detected with and without the filter) is highly dependent on energy so in order to accurately reconstruct the number of X-rays in space it must first be determined how many of them actually made it to the calorimeters. In order to test each filter without repressurizing and warming XQC to room temperature, a process that takes hours, I assisted in the building of a filter wheel that attaches to XQC.


    XQC picture with filter wheel
    XQC with filter wheel attached



    Filter wheel inside

    What the inside of the filter wheel looks like.



    Initial data received from XQC looked like this:

    initial data plot data legend

    This data was taken using a room temperature filter and the smallest aperture on the filter wheel. Each points corresponds to a different characteristic emission line of a different element; allows us to exactly determine the energy of the detected X-ray. We measured the blue data points; the red triangles were measured on a different X-ray detector and used for calibration; the green circles are a theoretical model of how the filter should behave, according to the manufactured specifications. The sharp drop off with energy of the observed data compared to the predicted model indicates that ice built up on the filters, a problem that XQC has encountered in the past. After carefully cooling down XQC while heating the filters, the plot looked like:


    heated data plot data legend

    which does not show evidence of ice. From these plots, models could be generated. Each filter is made of a layer of Aluminum, a layer of Polyimide, and a layer of Aluminum Oxide (as well as possible a layer of H2O ice). These vary between the filters. All of the filters have a silicon mesh and epoxy used to hold them in place, so this factor can be normalized away. The transmission function is given by

    nonlinear model with N line


    where ℓ stands for the e-folding length of a layer (the thickness of material required to reduce the transmission by a factor of 1/e) and d is the thickness of that layer. Si is the transmission factor due to the silicon mesh. The e-folding length, is a function of the energy of the X-ray. A nonlinear least-squares fit was performed on the function, giving a result. The fitting program we used runs in python and uses lmfit as its minimization routine. However, as can be seen below, the solution was highly dependent on each point in particular, as well as the what we told it were the lowest and highest possible thicknesses of each material, and therefore often gave nonsensical results. Furthermore, chi-squared values were often high, even for sensible fits.

    nonlinear model with N line
    nonlinear model without N line

    A model of a filter; the top plot includes a Nitrogen line, while the bottom plot excludes it. Thicknesses of each layer in Angstroms are included. The dramatic effect the exclusion of a single data point has makes the filter model less reliable and more prone to failure due to random error in the counting rates. Since the X-rays are produced by alpha particles from radioactive decay, this error is uncontrollable.
    In order to better model the filters, we switched from a nonlinear to a linear model. By taking the natural log of the transmission function (after normalizing by dividing out the Si term), we got:

    log equation

    for each elemental transition line with energy En.

    Because we only used discrete characteristic radiation lines, the e-folding length for each layer is not a continuous function but only takes on certain values. Therefore we could decompose the transmission function into a matrix,

    matrix transmission function

    where 1,2...n refers to the transmission and X-ray energy of a particular characteristic transition line of an atom. We could then solve the matrix equation for each d. Solutions were found using Mathematica's LeastSquares routine. Additionally, we could use this linear method for two of the thicknesses, and then use the nonlinear fit for the third (by fixing the values of the other two during the nonlinear fit) to see if this would give us better results.

    Comparison of Fitting Algorithms
    In order to better determine which fitting method to use, we applied each algorithm to data taken by an external calibration source and not XQC.


    Nonlinear Model:
    nonlinear model

    Linear Model:
    linear model

    Nonlinear Model, but using linear model to determine Al and O thicknesses:
    linear model to nonnlinear model

    Calibration Model:
    calibration fit


    The models give different results for about the same goodness of fit. While the fits are better than an older calibration fit, the models themselves are less realistic (1000 angstroms of polyimide is double what the manufacturer claims is on the filter, which is unlikely). A negative oxide thickness is unphysical; a better interpretation of the result is that the oxide layer is zero or negligible. The aluminum thicknesses, however, are all generally consistent with each other. Overall, the nonlinear fit still seems to give better results on the calibration data.


    Aitoff Maps


    One other project I also worked on was taking maps made in galactic coordinates (l,b) and projecting them on an Aitoff projection. This is done by taking a pixel in the Aitoff projection image, transforming it to (l,b) coordinates, finding the closest four points on the map, and computing the weighted average with the weight as 1/ angular distance to the pixel location. An example map, as well as a comparison to an existing map (taken by dividing each pixel value in the new map by the existing map) is shown below.

    Aitoff Map (arbitrary units):
    aitoff map example

    Comparison Map (% of reference map value):
    aitoff map comparison

    Any major differences (>2%) between the new and example map were determined to be due to differences in the algorithm used to construct the two maps and were confined to pixels where the map value changed rapidly. Using these maps, I was then able to simulate what the response would be if a collimator was exposed to a patch of the sky. To do this, I found every point in the map in the field of view of the collimator (for this simulation, seven or nine degrees) and summed their values using weights of magnitude collimator weight where θ is the angular distance between the point in question and the center of the collimator.

    References

    Boyce, K. (2001, May 16). Introduction to X-ray Microcalorimeters. Retrieved July 30, 2014, from http://phonon.gsfc.nasa.gov/rocket/intro/intro.html
    McCammon, D., & Sanders, W. T. (1990). The Soft X-Ray Background and Its Origins. Annual Review of Astronomy and Astrophysics, 28(1), 657–688. doi:10.1146/annurev.aa.28.090190.003301
    mim5. (n.d.). Solar Wind Charge Exchange — University of Leicester. Page. Retrieved July 30, 2014, from http://www2.le.ac.uk/departments/physics/research/xroa/astrophysics-1/SWCX
    Nave, R. (n.d.). X-rays. Retrieved July 30, 2014, from http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/xrayc.html
    Smith, R. K., Foster, A. R., Edgar, R. J., & Brickhouse, N. S. (2014). Resolving the Origin of the Diffuse Soft X-ray Background. arXiv:1406.2037 [astro-Ph]. Retrieved from http://arxiv.org/abs/1406.2037
    Soft X-ray Diffuse Background. (2012, October 4). Retrieved July 30, 2014, from http://imagine.gsfc.nasa.gov/docs/science/know_l2/diffuse_background.html
    The Diffuse High-Energy Background - Introduction. (2010, February 3). Retrieved July 30, 2014, from http://imagine.gsfc.nasa.gov/docs/science/know_l1/diffuse_background.html
    XQC. (n.d.). Retrieved July 30, 2014, from http://wisp.physics.wisc.edu/xray/xqc.html

    CSS "colourise" from http://www.styleshout.com/


    Research projects of other REU students
    Picture of Washburn Observatory