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301 | 301 | "source": [ |
302 | 302 | "### Extras\n", |
303 | 303 | "\n", |
304 | | - "* Now compare the total luminosity from all O stars to total luminosity from all M stars. This requires a mass-luminosity relation, like this one:\n", |
| 304 | + "* Now compare the total luminosity from all O stars to total luminosity from all M stars. This requires a mass-luminosity relation, like this one which you will use as $\\rho(m)$:\n", |
305 | 305 | "\n", |
306 | 306 | "$$\n", |
307 | 307 | " \\frac{L}{L_{\\odot}} (M) =\n", |
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313 | 313 | " \\end{cases},\n", |
314 | 314 | "$$\n", |
315 | 315 | "\n", |
316 | | - "which you will use as $\\rho(m)$\n", |
317 | | - "\n", |
318 | 316 | "* Think about which stars are producing most of the light, and which stars have most of the mass. How might this result in difficulty inferring stellar masses from the light they produce? If you're interested in learning more, see [this review article](https://ned.ipac.caltech.edu/level5/Sept14/Courteau/Courteau_contents.html)." |
319 | 317 | ] |
320 | 318 | }, |
|
326 | 324 | "\n", |
327 | 325 | "* Right now, we aren't worried about the bounds of the power law, but the IMF should drop off to zero probability at masses below .01 solar masses and above 100 solar masses. Modify `PowerLawPDF` in a way that allows both `float` and `numpy.ndarray` inputs.\n", |
328 | 326 | "* Modify the `PowerLawPDF` class to explicitly use `astropy`'s `units` constructs.\n", |
329 | | - "* Derive a relationship between recent star-formation rate and $H\\alpha$ luminosity. In other words, for the function\n", |
| 327 | + "* Derive a relationship between recent star-formation rate and $H\\alpha$ luminosity. In other words, find a value of $C$ for the function\n", |
330 | 328 | "\n", |
331 | | - "$${\\rm SFR \\, [\\frac{M_{\\odot}}{yr}]} = {\\rm C \\, L_{H\\alpha} \\, [\\frac{erg}{s}]} \\, ,$$\n", |
| 329 | + "$${\\rm SFR \\, [\\frac{M_{\\odot}}{yr}]} = {\\rm C \\, L_{H\\alpha} \\, [\\frac{erg}{s}]} \\, .$$\n", |
332 | 330 | "\n", |
333 | | - "find a value of $C$. How does this depend on the slope and endpoints of the IMF?\n", |
334 | | - " * Take a look at Appendix B of [Hunter & Elmegreen 2004, AJ, 128, 2170](http://adsabs.harvard.edu/cgi-bin/bib_query?arXiv:astro-ph/0408229)\n", |
335 | | - " * What effect does changing the power-law index or upper mass limit of the IMF have on the value of $C$?\n", |
336 | | - " * Predict the effect on the value of $C$ of using a different form of the IMF, like Kroupa or Chabrier (both are lighter on the low-mass end). If you're not tired of IMFs yet, try defining a new class that implements a broken-power-law (Kroupa) or log-parabola (Chabrier) IMF. Perform the same calculations as above." |
| 331 | + "* How does this depend on the slope and endpoints of the IMF?\n", |
| 332 | + "* Take a look at Appendix B of [Hunter & Elmegreen 2004, AJ, 128, 2170](http://adsabs.harvard.edu/cgi-bin/bib_query?arXiv:astro-ph/0408229)\n", |
| 333 | + "* What effect does changing the power-law index or upper mass limit of the IMF have on the value of $C$?\n", |
| 334 | + "* Predict the effect on the value of $C$ of using a different form of the IMF, like Kroupa or Chabrier (both are lighter on the low-mass end).\n", |
| 335 | + "* If you're not tired of IMFs yet, try defining a new class that implements a broken-power-law (Kroupa) or log-parabola (Chabrier) IMF. Perform the same calculations as above." |
337 | 336 | ] |
338 | 337 | } |
339 | 338 | ], |
|
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