radiative processes in astrophysics - wladimir lyra · course overview textbook: radiative...

Radiative Processesin Astrophysics

Quick Bio

Wladimir Lyra

B.Sc. in Astronomy, Federal University of Rio de Janeiro (UFRJ, Brazil), 1999-2003.

Research Assistant 2003-2004 Space Telescope Science Institute (STScI, Baltimore MD)Cerro Tololo Interamerican Observatory (CTIO, La Serena – Chile)European Southern Observatory (ESO, Munich – Germany)Lisbon Observatory, Portugal.

Ph.D. in Astronomy, Uppsala University (Uppsala, Sweden), 2004-2009. Nordic Institute for Theoretical Physics (NORDITA, Stockholm, Sweden) Max-Planck Institute for Astronomy (MPIA, Heidelberg, Germany)

Postdoctoral Researcher American Museum of Natural History (AMNH, New York NY), 2009-2011. Jet Propulsion Laboratory (NASA-JPL/Caltech, Pasadena CA), 2011-2015.

Stellar Astrophysics, Planetary SciencesSolar-type stars, extrasolar planets, star formation, circumstellar disks and planet formation. Hydrodynamics, plasma physics, turbulence, life in the universe, icy moons and Europa.

Course Overview

Radiative Transferand

Line Formation

Stellar Structure

Relativistic emission

Infrared to Radio

Interaction of radiation and

magnetic fields.

Course Overview

Textbook: Radiative Processes in Astrophysics, Rybicki & Lightman

We will also use:Astrophysics for Physicists, Choudhuri

An Introduction to Modern Astrophysics, Carroll & Ostlie.

Course Overview

Grading

Homework (1/3)

Checkpoints (1/3)

Final exam (1/3)

Electromagnetic Spectrum

Order of magnitude estimate

Let’s estimate the size of the following quantities:

Government in dollarsK-12 education

Size of entertainment industryRestaurant industry

Problem from Eugene Chiang’s course Order of Magnitude Physics


Government size in dollars

Government revenues are from taxes. The population of the country is 3x108 persons. The country’s per capita is $55k. For an average tax of 30%, the total revenue is

3x108 x 5.5x104 x 0.3 = 4.95 trillion dollars

Looking up the data, the government budget in 2015 was 3.8 trillion dollars. Our estimate is well within a factor 2.



K12 education

What is the size of K12 education in the country? We can estimate this number by identifying the biggest chunk. In this case, it should be the teacher’s salaries. Quickly looking up the data shows that the average salary of a K12 teacher is $50k. With benefits and retirement, that should add up to $100k. How many of them we need to pay? K12 age ranges 6-18. For a lifespan of 80 years, means that 12/80 of the population is in K12. That means 12/80 x 3x108 = 45 million kids. With 25 kids per class, we need 1.8 millions teachers. So, the size we estimate is 1.8x106 x 105 = 180 billion dollars. Looking up the data, the real number is closer to 500 billion dollars. Clearly more goes into K12 than just teacher’s salaries (rent, books, food, etc), but our estimate was close by a factor of less than 3.



Entertainment industry

How much money does the entertainment industry move? We could try the same way we did with K12 education, identifying the big chunk, but so many of these industries (movie, music, etc) seem to play significant roles. So, we take another approach. Estimate how much money one spends on entertainment, and extrapolate from that. I myself spend perhaps $50 a month with internet and netflix, plus $20 a week with cinema, reading, or music. That’s about $130 a month. Taking that to be representative of the population, that amounts to $130/months x 12months x 3x108 = 470 billion dollars. Now, that’s just me, and my salary is lower than average. But even if I made more money, I doubt I would spend more than that, just on time constrains. Assuming most of the country is as busy as I am, that number should be representative. So, we’ll go with 470 billion dollars. The data on the next page shows it to be 595 billion dollars. Not far off the mark.



Restaurant industry

How much money does the restaurant industry move? Let’s estimate this number the same way we did with the entertainment industry, extrapolating from oneself. I eat out for lunch or grab a quick dinner maybe twice a week on $10 each. Plus maybe a dinner a week on $30. That’s 50 dollars per week. For 52 weeks a year, that amounts to $2600 a year. If that’s typical, then the whole country (3x108) should spend 780 billion dollars a year on restaurants. The data next page shows the true number to be $709 billion.


An age old question…

Are there more stars in the Universe than the number of grains of sand on the beaches of Earth?

A tough question, but we can answer it by using the same tools we used for the previous ones. Let’s start with the easy number: stars in the universe. We know there are about 100 billion stars in the Milky Way, and about 100 billion galaxies in the Universe. That amounts to 1011 x 1011 = 1022 stars in the Universe.

As for grains of sand on the beaches of Earth? A grain of sand is about 1mm in radius, so the volume of a grain is 4/3πr3 ~ 4 mm3 = 4x10-3 cm3 = 4x10-9 m3. Now what is the volume of all beaches of planet Earth? Tough number to estimate. Or is it? Let’s consider Santa Monica or Venice Beach. It has about 50 m of sand extension. Let’s say the depth is half of it, i.e., 25m. So, width times depth is 50x25= 1250m2. How about the length? Let’s say all shorelines of the continents are beaches. Looking at the shape of the continents, we can say that the perimeter of each continent is about as large as the equator (the circumference of Earth). Earth having 7 continents, that amounts to 7 x 2π x 6000 km = 2x108 m. So, the volume of all beaches on Earth is 2x108m x 1250m2 ~ 3x1011 m3. So, the number of grains of sand is the volume of all beaches divided by the volume of each grain = 3x1011 m3 / 4x10-9 m3 = 7.5x1019 ~ 1020. So, there are about 100 times more stars in the Universe than grains of sand on all beaches of Earth.

radiative processes in astrophysics - wladimir lyra · course overview textbook: radiative...

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