more Lab 3 updates
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Maxwell Millar-Blanchaer
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1 changed files with 154 additions and 3 deletions
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@ -32,7 +32,7 @@
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Read through this entire lab before you start. In this lab, we will look at the brightness of stars as measured in astronomical units called ''magnitudes.'' To complete this lab you should have already read textbook Chapter 3 and Sections 2.3 and 2.4. "
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"Read through this entire lab before you start. In this lab, we will look at the brightness of stars as measured in astronomical units called ''magnitudes.'' To complete this lab you should have already read textbook Chapter 3 and Sections 2.3 and 2.4. In this lab, you will be asked to type out some equations. In a jupyter notebook you can do this using standard LATEX math notation. If you're new to LATEX you can use [this online equation editor](https://latex.codecogs.com/) to help you along to start. Later in this course you'll be using La"
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@ -362,7 +362,158 @@
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"For telescopes on the ground, the FWHM is usually set by atmospheric turbulence and is called ``seeing.'' A better site gives a shaper image. \n"
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"For telescopes on the ground, the FWHM is usually set by atmospheric turbulence and is called ''seeing.'' A better site gives a shaper image. \n"
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]
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},
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"\n",
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"## <p style=\"text-align: center;\">Part 3: Backgrounds and Photon Noise</p>\n"
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"The ```BACKGROUND``` column in ```cluster1.cat``` contains estimates of the sky background flux (per pixel) in the neighborhood of each identified object. **Make a scatter plot of the sky background as a function of ```X_IMAGE```, using any plot symbols you like, but without lines connecting the points.**"
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]
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"#Your code here"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"What happens if you do use lines to connect the data points? **Explain what the program is doing to generate this unusable plot.**"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"#Your code here"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"*Your answer here*"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"**What is a typical value for the sky background? What is the approximate scatter in the reported values?**"
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]
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{
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"cell_type": "code",
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"execution_count": 1,
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"metadata": {},
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"outputs": [],
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"source": [
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"#Your code here"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"*Your answer here*"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Within Python you can calculate simple statistics (min, max, mean, standard deviation) for data sets using ```numpy``` functions. Ordinarily, your visual impression of the typical value of a bunch of plotted data points will closely approximate the mean value, and your visual estimate of the peak-to-peak scatter (ignoring rare outliers) will be roughly 4 times the standard deviation. How do mean and standard deviation computed with Python compare with the visual estimates you just made?"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"metadata": {},
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"outputs": [],
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"source": [
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"#Your code here"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"*Your answer here*"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"\n",
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"**Now, make a scatter plot ```MAGERR_ISOCOR``` as a function of ```MAG_ISOCOR```.** ```MAGERR_ISOCOR``` is an estimate of the error in ```MAG_ISOCOR```, based on square-root-rule counting error for the number of detected photons in the object plus the underlying sky background (derived from the Poisson distribution). The total number of sky+object photons is\n",
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"$$\n",
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"N_{\\rm phot} = {\\tt GAIN} \\cdot ({\\tt FLUX\\_ISOCOR} + {\\tt BACKGROUND} \\cdot N_{\\rm pix})\n",
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"$$\n",
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"Where ````GAIN```` is the number of detected photo-electrons per signal count (2.36 $e^-$/count for this image, determined from the ```EGAIN```\n",
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"keyword in the FITS header). $N_{\\rm pix}$ is the number of pixels occupied by the object image. With ```ISOCOR``` photometry this number is hard to know for sure, but a reasonable guess is $\\pi ({\\rm FWHM}/2)^2$. **Use this guess, the ```GAIN``` value just given, and your estimate of ```BACKGROUND``` to write an expression for $N_{\\rm phot}$ as a function of ```FLUX_ISOCOR```.**"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"#Your code here"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"*Your answer here*"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"**Now use the flux-vs-magnitude expression from page 2 to write an expression for $N_{\\rm phot}$ as a function of ```MAG_ISOCOR```.**"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"*Your answer here*"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"The expected counting error (measured in photo-electrons) is the square root of $N_{\\rm phot}$. To get the noise in units of counts, we must\n",
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"divide by the ```GAIN```. **Write an expression for this counting error as a function of MAG_ISOCOR}.**\n"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"*Your answer here*"
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]
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},
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{
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@ -387,7 +538,7 @@
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.8.8"
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"version": "3.7.3"
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}
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},
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"nbformat": 4,
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