Lab 3 draft finished

Lab 3/Lab 3.ipynb

@@ -519,7 +519,111 @@
   {
    "cell_type": "markdown",
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-   "source": []
+   "source": [
+    "Now the tricky part. **What error (in magnitudes) is implied by this error in the measured value of $N_{\\rm phot}$?** Assume that the error is small\n",
+    "compared to $N_{\\rm phot}$ itself (i.e., that $N_{\\rm phot} \\ll 1$), and show that if\n",
+    "$$\n",
+    "{\\rm mag} = m_1 - 2.5 \\log_{10}({\\rm flux})\n",
+    "$$\n",
+    "(where $m_1$ is the magnitude that yields ${\\rm flux} = 1$), then\n",
+    "$$\n",
+    "\\delta {\\rm mag} \\approx 1.086 \\frac{\\delta {\\rm flux}}{\\rm flux}.\n",
+    "$$\n",
+    "Derive this expression below.  You may use standard propagation of uncertainties and take the square root."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "*Your equation here*"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "**Now combine this expression and the one for counting error to write an expression for the expected error in magnitudes as a function of the object magnitude.**"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "*Your equation here*"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "**Finally, define integer magnitudes covering the range of magnitudes in ```cluster1.cat```:**\n",
+    "\n",
+    "```x = np.arange(int(np.amin(mags)), int(np.amax(mags)) + 1)```\n",
+    "\n",
+    "**and evaluate your expression for magnitude uncertainties at these integer ```x``` values.  Overplot this on your plot of ```MAGERR_ISOCOR``` vs.~```MAG_ISOCOR``` using a thick, red line.**"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "\n",
+    "## <p style=\"text-align: center;\">Part 4: Consistency and Systematic Errors</p>\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Now we know how to use Source Extractor output to estimate the fluxes and magnitudes of stars, and also the precision that simple physics says we should be achieving. But how well do we know our errors, really? Might effects other than photon counting statistics be dominant? And what about systematic errors, which give us consistent and repeatable wrong answers? How can we test for these?\n",
+    "\n",
+    "\n",
+    "Source Extractor can estimate source fluxes in several ways – two of these are isophotal photometry (which deals well with objects having funny shapes) and aperture photometry (which works well for perfectly round objects, as star images are supposed to be). Check section 7.4 of *Source Extractor for Dummies* for an explanation of what these things mean. The picture on p.~41 is particularly helpful.\n",
+    "\n",
+    "\n",
+    "Since there are different ways to estimate what ought to be the same quantities, let’s see if we get the same answers with aperture photometry as we did with isophotal photometry. If not, the differences tell us something about our errors. \n",
+    "\n",
+    "Make a figure with two graphs, one on top of the other. For this task, you'll want to use subplots sharing the $x$-axis (read the documentation page for ```pyplot.subplots```).  On the top axes, plot ```MAG_ISOCOR``` on the $x$-axis and ```MAG_APER``` on the $y$-axis. You should expect a tight but not perfect correlation between the two measurements, with a few dramatic outliers. The wide range in plotted magnitudes makes it hard to see the errors. **On the lower graph plot ```MAG_ISOCOR``` on the $x$-axis and, on the $y$-axis, plot (```MAG_ISOCOR – MAG_APER```). Choose your y-axis plot range carefully, to show the most information.\n",
+    "If necessary, sacrifice a few outliers to show the typical scatter better.**"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "#Your code here"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "What is the peak-to-peak scatter in the difference (```MAG_ISOCOR - MAG_APER```), if you ignore extreme outliers? How does this compare with the tabulated uncertainties ```MAGERR_ISOCOR``` and ```MAGERR_APER```? What do you conclude from this?"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "*Your answer here*"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Identify the stars corresponding to 3 of the most extreme outliers in your upper plot, and look at them using ds9. Can you describe the potential source(s) of these systematic errors?"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "*Your answer here*"
+   ]
   }
  ],
  "metadata": {
@@ -538,7 +642,7 @@
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