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Mapping the Universe Measuring Distances with Standard Candles Imagine that you find a star with an unknown distance, but you notice that it has a distinctive characteristic that tells you that it is a specific type of star. And let’s imagine that all stars of that type have the same luminosity, and you happen to know the value of that luminosity. You can then estimate the distance for the star you found from the inverse square law of light: b = L / d2 where b is the brightness seen from Earth L is the luminosity that all stars of this type are known to have d is the distance. Objects that are distinctive and have known luminosities are standard candles. Estimating distance with a standard candle measured expected value from Earth L b 2 solve for d The Distances to Galaxies with Cepheids In the lecture on the Milky Way, we used RR Lyrae stars as standard candles for measuring distances in our galaxy, but most galaxies are too far away for telescopes to detect RR Lyrae stars within them. Like RR Lyrae stars, Cepheid stars also pulsate in a regular fashion, which makes them easy to identify, and have known luminosities, so they too act as standard candles. Because Cepheids are brighter than RR Lyrae stars, they can be detected at larger distances, even in other galaxies. The Cepheid Period-Luminosity Relation Unlike RR Lyraes, Cepheids have a wide range of luminosities. But brighter Cepheids have longer pulsation periods, so if we measure how fast a Cepheid pulsates, we can deduce its luminosity from the relation shown below. The Distance Ladder Cepheids 100 milllion ly RR Lyrae 10 million ly parallax 1000 ly Earth Distance Using Cepheids as a standard candle, we can measure distances to galaxies out to 100 million light years (ly). If we want to reach galaxies beyond that limit, we will need additional methods of measuring distances. The Tully-Fisher Relation The rotation speed of a galaxy depends on its mass (as we found when discussing dark matter). Galaxies with higher masses generally have higher luminosities. So the luminosities and rotation speeds of galaxies are correlated, which is know as the Tully-Fisher relation. So using the Tully-Fisher relation, we can estimate a galaxy’s luminosity by measuring its rotation speed, and then use that luminosity to estimate the distance of the galaxy. The Distance Ladder Tully-Fisher 600 million ly Cepheids 100 million ly parallax 1000 ly Earth Distance RR Lyrae 10 million ly Type Ia Supernovae If a white dwarf gains enough matter from another star so that its mass exceeds 1.4 M, it experiences a Type Ia supernova, which is bright enough to be seen in distant parts of the universe. These supernova always have the same luminosities, and therefore can be used as standard candles for measuring distances to the most distant galaxies. The Distance Ladder Type Ia Supernovae 3 billion ly Tully-Fisher 600 million ly Cepheids 100 million ly parallax 1000 ly Earth Distance RR Lyrae 10 million ly Mapping Galaxies in the Universe Galaxies are not scattered randomly in space. Most galaxies are in groups and clusters. These clusters are arranged in walls and filaments that are separated by huge voids. Mapping Galaxies in the Universe Mapping Galaxies in the Universe The Origin of Structure in the Universe Stars form from the gravitational collapse of ripples and clumps in gas and dust clouds. Galaxy clusters formed in a similar manner after the Big Bang, but on a far larger scale. 100 Mly Age of universe = 0.2 billion years The Origin of Structure in the Universe Because it makes up most of the mass in the universe, dark matter played a crucial role in this process. Clumps of dark matter acted as the seeds that led to the formation of galaxies. 100 Mly Age of universe = 1.0 billion years The Origin of Structure in the Universe The formation of galaxies probably would not have occurred without the presence of dark matter. 100 Mly Age of universe = 4.7 billion years The Velocities of Galaxies In 1912, Vesto Slipher obtained spectra of galaxies, which he used to measure their velocities through the Doppler shift of absorption lines. The Velocities of Galaxies Moving Toward Us (blueshifted) Moving Away From Us (redshifted) The Hubble Law Edwin Hubble measured distances to Slipher’s galaxies. He found that galaxies with higher velocities away from us (higher redshifts) have larger distances from us. This correlation between distance and velocity is known as the Hubble Law. But it’s very unlikely that we are at the center of the universe, so why are all of the galaxies moving away from us? 1.5 3 (billion light years) The Expanding Universe At any location in a universe that is expanding, galaxies that are farther away will appear to be moving away faster. In other words, the Hubble Law would be observed by everyone in an expanding universe. Rather than indicating that we are at the center of the universe, the Hubble Law tells us that the universe is expanding. So galaxies are not flying apart into the universe. The universe itself is expanding. The galaxies are simply riding along as the fabric of space expands. The Expanding Universe The expansion of the universe also causes light to get stretched to longer wavelengths, or redshifted. So the redshifts that we measure for galaxies are not due to their velocities away from us, but instead result from the expansion of the space itself. The Cosmological Constant Einstein believed that the universe was static and unchanging. However, gravity should eventually cause a static universe to collapse. He didn’t like this idea, so he proposed the existence of anti-gravity, which he called the Cosmological Constant, that would prevent the universe from collapsing. The Cosmological Constant Shortly after Einstein developed the Cosmological Constant, Hubble discovered that the universe isn’t static, and instead is expanding. So Einstein was wrong to assume the universe is static, and it wasn’t necessary to invent anti-gravity to maintain a static universe. He referred to the Cosmological Constant has his “greatest blunder”. 1.5 3 (billion light years)