Planck and Cepheids: new problems?


Some of the biggest news in astronomy and cosmology is the recent announcements of results from the Planck mission that observed the cosmic microwave background. One of the key results is that the universe is actually a bit older than previously estimated, now 13.82 billion years old as opposed to 13.73 billion years old. What’s 100 million years difference matter in the grand scheme?

Well it is not the age that is the challenge but the expansion rate of the universe or what is called the Hubble Constant. The universe is known to be expanding, for instance when we look at far away galaxies we observe them to be moving away from us and galaxies twice as far are moving twice as fast. This rate tells us about the age of the universe and how much mass and energy is in the universe. The Planck mission found the rate to be 67.3 km/s/Mpc (1 Mpc (megaparsec) = 100000 parsec = 3,260,000 light years). This is interesting, the predecessor to Planck, the WMAP mission measured about 72 km/s/Mpc while other methods measured about 72 - 75 km/s/Mpc.

It is surprising that Planck is so much lower and raises a few questions about these other methods. The best other method employed so far requires measuring the velocity of far off galaxies using their spectra and searching for standard candles in those galaxies to measure distances. When an object is moving and emits light, light at various wavelengths will be shifted, an object moving away appears redder than it would if it were not moving. By measuring how much the light is shifted then we can measure the speed of a galaxy. This is analogous to how the sound of a train changes when it is traveling towards and away from an observer.

Measuring the distances to these galaxies requires finding standard candles. A standard candle is an object that, when observed, allows astronomers to measure the distance to that object. The most commonly employed standard candle is a Cepheid, a personal favourite of mine that I have studied since my PhD. A Cepheid is a variable star whose brightness oscillates for a few days up to 200 days, and that period of oscillation is a direct measure of how much light a Cepheid is emitting. By observing how bright a Cepheid appears and its period, hence its actual brightness, we can measure the distance to that star and the galaxy in which it lives. It is these objects that have been primarily used to measure the Hubble Constant and the best
measurements suggest a greater rate of expansion than the new Planck results.

What does this mean? Could Planck be in error? Or Is there something we are missing in understanding these favoured standard candle? Perhaps Planck is telling us that we need to better understand these stars and that we need to revisit them in greater detail. This is difficult challenge and I am stymied how the Cepheid measurements might be so off. It is important to figure this out because Cepheids will provide an independent check of the Planck results when the James Webb Space Telescope comes online and astronomers will be able to observe Cepheids at unprecedented distances with unprecedented accuracy.

The newly-released Planck results are a giant leap forward in the understanding of the beginning of the universe and the results have consequences throughout the field of astronomy, even to the seemingly unrelated field of stellar physics. But Planck might just be requiring us to rethink what we know about these stars. For every answer, more questions arise; this is why science is awesome.
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Cepheids and Winds, Part II

In Part I, I discussed how Cepheid variable stars are awesome tools for understanding stars and cosmology and how one particular property, the change of the pulsation period, is leading to new and exciting understanding of these stars and how it is leads to a new problem in understanding these stars. In this part, I want to present a hypothesis for solving this problem.

The problem is that we observe that about 2/3 of Cepheids in our galaxy have increasing pulsation periods and 1/3 decreasing pulsation periods and that when we compare this ratio to the "standard" stellar evolution models we find a discrepancy. From the models we predict that 85% of Cepheids should have an increasing pulsation period.

This problem means that the physics assumed in our models must be incomplete and there are two candidates to resolve the discrepancy. The first is called convective core overshoot and the second is a enhanced stellar wind. Stars that are more massive than about 1.5 times the Sun have convective centers where nuclear reactions occur and energy is created. These convective centers are analogous to water boiling in a pot, boiling water bubbles and the bubbles move from the bottom of the pot to the top then release heat and steam. If you put a lid on top of a pot of boiling water, the water will generate enough force to boil over. Convection in stars is difficult to simulate and requires 3 dimensional modeling, simulating time scales less than a day, stellar evolution models are typically one dimensional and simulate time scales of thousands of years at the shortest. It is just very difficult and impractical to simulate both together right now. So to simplify things, astronomers treat convection and convective energy transport using one basic relation. But this relation is not physical so we also add a free parameter to account for the "boiling over" of the convective center, where convective bubbles push into layers just above. For Cepheids, this "boiling over" parameter makes them brighter and have larger radii

The second possibility is a strong stellar wind that decreases the mass of the star and can change the radius of the star as well, although this feedback is not well understood. A wind might increase the radius by acting as an additional pressure that balances against gravity. By decreasing the mass, a stellar wind directly changes the pulsation period.

We can test these hypotheses directly by adding the physical theories to our stellar models and then counting what fraction of Cepheids have increasing periods and what fraction negative. In the first test, we add convective overshooting, and show the plot below. The black dots are the observed rates of period change while the color contours are the predicted rates. There is some agreement but still not overly great. The predicted fraction of Cepheids with increasing periods is 85%.... again. This is the same fraction as I showed for the standard models in Part I. Playing with the convection doesn't change this ratio!


For the second test we computed Cepheid evolution models with a strong wind, a wind where a Cepheid would lose about 1/10 of the Earth's mass every year. Over a typical lifetime of a Cepheid this could be as much as one Sun worth of mass. I show the results below, the points and color contours have the same meaning. The agreement still isn't great but the predictions wildly differ from the other predictions. What is more, from the models with strong stellar winds, we predict that 71% of Cepheids have increasing periods and 29% have decreasing periods. This is pretty good agreement with the observations and is the first direct evidence that Cepheids in general.

This result is exciting because we are exploring new territory in our understanding of Cepheids and are probing a new piece of the puzzle that is understanding stellar evolution. This also means that we can verify the infrared observations of Cepheids having a stellar wind. The most exciting part of this research is not that it just solves a problem but also raises a number of other questions. How do Cepheids lose mass in a wind? Is it related to pulsation or something else? How does this wind vary from Cepheid to Cepheid? Is it a function of pulsation period like the luminosity? If mass loss leads to "extra" infrared light, how does this mass loss affect the Cepheid's ability to be standard candles at these wavelengths? If mass loss is so large, does it occur in other pulsating variable stars or stars of similar temperature but more massive that will eventually explode as supernovae? This is simply the beginning.

PS: While I think this result is exciting and new, my favorite part of this work is that it is science at its simplest and best. Science is about identifying a problem, suggesting a hypothesis to solve that problem then testing that hypothesis. If the hypothesis fails, you go back to drawing board and come up with a new idea then try that. We repeat and repeat until the hypothesis succeeds and science progresses. That's what this project is, a problem where observation of period change disagree with theory. Then a hypothesis where we test convection and that hypothesis fails. Then a new hypothesis of a strong wind, lo and behold the new theory agrees with observations and science progresses. Welcome to science.
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New Move, New Work


Astronomy and academia are tough careers, there are not too many job available at any one time and they are in many places. I have finished an amazing three years in Bonn at the Argelander Institute for Astronomy and am now beginning a new job in Johnson City, Tennessee at East Tennessee State University. My new job is a great opportunity to develop into a better astronomer as well as being closer to my family than I was before.

I have been nervous about moving here, Johnson City is not the most famous nor largest city. I really did not know what to expect in living here, except that it is a less urban city than say Nashville or Boston or Bonn. I expected it to be a quiet city and a bit more rural than I have been used to.

But, I arrived to a vibrant city surrounded by mountains and forests. There are trees all around in their autumn finery displaying many shades of red and green. Everyone I have met so far are friendly and outgoing, making me feel at home. The university is scenic with a blue buccaneer as the mascot. My new workplace seems great. It is far from the largest astronomy research group, but the faculty are certainly enthusiastic and productive. I haven’t been there a whole week yet, but research ideas are popping up everywhere. It is an energizing research environment.

So far, it has been a good move, but wow, there were so many things to be done. Thankfully, my lovely wife helped me out and gave me lots of support. I owe her so much. There was the work visa, the social security number, health insurance, etc., I could have been buried alive by paperwork. There was the flight, bringing only a couple of bags and setting up It is mostly done now, and I can focus on new science and astronomy.

I am excited to be working at ETSU, starting new projects understanding massive stars, magnetic fields and polarized starlight, and I look forward to experiencing the local culture and flavor. But, I still don’t understand why the mascot of a university in a landlocked city and state is a blue pirate.
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Cepheids and Winds

Classical Cepheids are one of the most important workhorses for astronomers. These stars help us understand the insides of stars and how stars change with time. Cepheids also help us understand the structure of the universe. More than a century ago, Henrietta Leavitt discovered that Cepheids can be used to measure distances to objects and soon after Edwin Hubble used Cepheid observations to help discover that the universe is expanding, creating a whole new understanding of the universe.

Nowadays, Cepheids are not used as often for studying cosmology; other techniques are now more precise. But using the upcoming James Webb Space Telescope and the next generation of extremely large telescopes that will observe at infrared wavelengths, Cepheids will contribute again to cosmology as well as to our understanding of the structures of stars. However, that is the future; recent observations are raising new questions of our understanding of Cepheids and stars in generals, observations that may limit how well infrared observations of Cepheids will contribute to better measuring the expansion of the universe.

In 2006, a group of astronomers (Kervella et al. 2006, A&A, 448, 623) reported the detection of "extra" light from nearby Galactic Cepheids at near-infrared wavelengths near 2 microns. It was not obvious where this extra light comes from, but the authors suggested that it is a from a strong wind emanating from the Cepheid, a wind that no one had expected. Such a wind affects how the star evolves and potentially the formation of white dwarf stars and even supernovae that Cepheids will eventually become. More evidence has been reported in articles by myself and by other groups. The challenge now is to use other methods to understand if there is a Cepheid wind and then understanding how this wind affects the properties of Cepheids.

The key property that makes Cepheids powerful tools for understanding stars and cosmology is pulsation. Cepheids pulsate, meaning that a Cepheid's brightness increases and decreases and repeats over a regular and repeatable time scale, typically between a few days and about 100 days. Ms. Leavitt discovered that this pulsation period is related to how much light a Cepheid emits. By observing the period, we can now how bright the Cepheid actually is and by comparing that to how bright it appears, we measure its distance. It is this property that Edwin Hubble used to help discover that the universe is not static.

The pulsation period is also related to the interior structure of the star. The same physics that describes a oscillating string or the sound in a pipe organ also describes a Cepheid. If you tie one end of a string to a hard surface and shake the other end until a standing wave forms then the period of that wave depends on the length of the string as well as the tension in the string, like if it is twine or wool, etc. Similarly, the pulsation period in a Cepheid is a function of the star’s mass and radius, which in turn are functions of the interior physics and any potential stellar wind. So, if we measure the pulsation period we can make models of the current structure of a Cepheid and potentially explore the existence of stellar winds.

While that itself is remarkable, astronomers (Turner et al. 2006, PASP, 118, 410) have also found that pulsation periods observed over a long time, from decades to about 200 years, are changing. Just as the pulsation period measures the inside of a Cepheid, the change of the pulsation period measures the changes in the inside of a Cepheid, i.e. the evolution of a Cepheid. Stars like the Sun will live for billions of years and we will not see them change in a few human life times. The most massive stars live for a few million years, we will not see them change, but we can observe, in real time, the evolution of Cepheids.

We can take our theoretical understanding of stars and computed models of Cepheid evolution and directly compare with the observations of period change. We can compare models and observations of stars evolving. This allows astronomers to test various theories of convection in stars, stellar winds, whatever pet theory you can devise. We can use the change of pulsation period to verify the observations of stellar wind discussed above.

But, it gets even better. The observations of period change in Cepheids go two ways, Cepheid periods are observed either to get longer or get shorter. Turner et al. compiled a list of almost 200 Cepheids in our galaxy, about 2/3 of the Cepheids have periods that are getting longer, while the remaining 1/3 having periods that are getting shorter, Those with periods getting longer are either losing mass, or are getting bigger, i.e. larger radius. We know the Cepheids might be losing mass, but we are sure these stars are expanding, or maybe a combination of the two. Similarly, those Cepheids with decreasing periods are contracting. By computing a population of Cepheids in our galaxy and predicting the relative number of models with increasing and decreasing pulsation periods we can test our understanding of the physics of stars. Just by comparing two numbers!

In the picture below, the period change as a function of how much light Cepheids emit is plotted. The dots are rates of period change of observed Cepheids and the color squares represent predictions from theoretical models of stellar evolution assuming no "extra" physics. The results are okay, they do not appear to overlap much, but there is also a lot of uncertainty in the measurements, so we cannot take this picture too seriously. What can take seriously is the predicted fraction of Cepheids with increasing period, ~85%. That is much larger than the observed fraction of 67%. There is something missing in models used in that plot. We have a problem!


In Part II, I suggest a couple of solutions and present the comparisons.
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Weighing Stars From their Light: Stellar Limb Darkening and Masses

Stars, like planets, have atmospheres. A stellar atmosphere is the outer layer of a star where light is escapes the star. Light is created in the core of a star from nuclear reactions, that light interacts with atoms in the star, being absorbed and reemitted, until the light is close to the surface of the star where it stops interacting and can travel into empty space. But that light tells us about the temperature at the surface of the star as well as the star’s composition. We can simulate these out layers and simulate how much light is emitted at various wavelengths. Astronomers have computed these models for 40 years or so.
Nowadays, observations using multiple telescopes working together called interferometry, or observations stars that eclipse each other allows astronomers to measure the light being emitted from different parts of the surface of a star. This is called limb darkening. Star appears brightest at the center and dimmest near the edge, just like the Sun. This limb darkening depends on how the temperature varies as function of depth from the surface of the star. In computer simulations, it also depends on the assumed shape of the star.
Historically, stellar atmosphere models assume that the atmosphere has depth much much smaller than the diameter of the star. In that case, one could assume the stellar atmosphere is a plane-parallel atmosphere. This kind of model assumes star has shape of an infinitely wide slab, and is a reasonable approximation for stars like the Sun but not stars like Betelgeuse. Another possibility is to assume that atmosphere is spherically symmetric, these models have been studied for decades but it is only in the past few years where we could easy compute thousands of these models for statistical studies.

Coefficients from a limb-darkening law as function of the stellar radius and mass from spherically-symmetric model stellar atmospheres for various stellar temperatures, red circles is 3000 Kelvin, green squares are 4000 K, blue circles 5000 K, magenta triangles 6000 K and blue triangles 7000K. The black crosses are predictions from plane-parallel models assuming a mass of 5 times that of the Sun.

In my new article I compute limb darkening profiles for about three thousand model stellar atmospheres at various wavebands from wavelengths just smaller than can be seen by one’s eyes up to the infrared. I then fit these profiles by a simpler polynomial relation that is commonly used to constrain observations of eclipsing binary stars or microlensing observations or interferometric observations, all of which allows us to resolve a stellar disk.
The simple law used in my work has two free coefficients that are fit, and we find that for spherically-symmetric model atmospheres the coefficients depend on the properties of the atmosphere including the ratio of the stellar radius and mass, as shown in the graph. Plane-parallel models do not carry information about this ratio, but we can use spherically-symmetric models to measure the ratio of the radius and the mass. This correlation between the limb-darkening coefficients and stellar properties can be used to compare to observations and measure that star’s mass. Measuring the mass is important because it is one of the most difficult properties to measure but one of the most important for understanding the nature of stars.
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Why is Astronomy Useful?

I once met a nice fellow, who was a rather practical down-to-earth kind of guy. He was retired but worked at a number of things before, all about taking care of his family and what not. While chatting, he asked me why is studying astronomy useful to the world? I was somewhat floored by this question and could not give him a good answer. I have been thinking about it ever since.

“Why is astronomy useful” is a difficult question to answer. If someone asks if what is the purpose of police officers or doctors, the answer is simple and quantifiable. I mean police officers protect people and doctors help keep people alive. Astronomy is not quite like these things and the aspect of astronomy that I research even more so. I study stars and their light, but not stars like the Sun, stars that are much more evolved and further away. What do I say to a person who asks me why this is useful?

I choose to look at it this way. I had a professor who very aptly described astronomy as a privilege and I think this is true for most of academia, from english to history to physics and math. Researchers are privileged. A few hundred years ago, I would never be able to study astronomy, I’d be more focused on trying to stay fed and not die of a stubbed toe. If I were born in one of the poorer countries of the world, I would have no time to look at the stars, but might need to beg for enough food to stave off starvation. Academia is a privilege allowed to those in richer countries that give children access to education or to rich people who can afford to buy it. In this respect, I am very lucky that I can spend time learning about stars and galaxies that cannot even be seen with the human eye.

But the ability to study astronomy and the natural sciences, in general, is more than just a privilege. It is a gateway to innovation and invention, even when that is not the intent of the research. A great example comes from Albert Einstein, who predicted that when a photon of light of a certain wavelength interacts with an atom that has electrons orbiting at an energy level that is not the ground state. The photon stimulates the electron to moved from its excited level to a lower level and hence emit another photon. This new photon has the same energy, i.e. wavelength and travels in precisely the same direction as the original photo. So now, instead of one photon there is two. This doesn’t sound that useful, until you consider a one photon traveling though a tube of gas of these atoms. Each photon interacts with an atom and more photons are created, and more interactions lead to more photons. All of these photons travel in the same precise direction, forming a collimated beam or a laser. Einstein proposed his idea in 1917, and the laser was invented in 1960, more than forty years later and lasers are now everywhere. Astronomy and natural science grow knowledge and this sparks innovation.

But it is not only about inventions and patents and money. Astronomy and other sciences and humanities are important because of humans. We are curious bags of water that have innate desires to understand the world about us. Astronomy is just one vehicle towards this end
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Limb-darkening as a test of stellar atmospheres

Just had a paper accepted for publication in Astronomy & Astrophysics on “Limb-darkening as a test of stellar atmospheres with Dr. John Lester from University of Toronto Mississauga. The abstract is

Context. Stellar limb darkening, I(μ = cosθ), is an important constraint for microlensing, eclipsing binary, planetary transit, and interferometric observations, but is generally treated as a parameterized curve, such as a linear-plus-square-root law. Many analyses assume limb-darkening coefficients computed from model stellar atmospheres. However, previous studies, using I(μ) from plane- parallel models, have found that fits to the flux-normalized curves pass through a fixed point, a common μ location on the stellar disk, for all values of T eff , log g and wavelength.
Aims. We study this fixed μ-point to determine if it is a property of the model stellar atmospheres or a property of the limb-darkening laws. Furthermore, we use this limb-darkening law as a tool to probe properties of stellar atmospheres for comparison to limb- darkening observations. Methods. Intensities computed with plane-parallel and spherically-symmetric Atlas models (characterized by the three fundamental parameters L, M and R) are used to reexamine the existence of the fixed μ-point for the parametrized curves.
Results. We find that the intensities from our spherical models do not have a fixed point, although the curves do have a minimum spread at a μ-value similar to the parametrized curves. We also find that the parametrized curves have two fixed points, μ1 and μ2, although μ2 is so close to the edge of the disk that it is missed using plane-parallel atmospheres. We also find that the spherically- symmetric models appear to agree better with published microlensing observations relative to plane-parallel models.
Conclusions. The intensity fixed point results from the choice of the parametrization used to represent the limb darkening and from the correlation of the coefficients of the parametrization, which is a consequence of their dependence on the angular moments of the intensity. For spherical atmospheres, the coefficients depend on the three fundamental parameters of the atmospheres, meaning that limb-darkening laws contain information about stellar atmospheres. This suggests that limb-darkening parameterizations fit with spherically-symmetric model atmospheres are powerful tools for comparing to observations of red giant stars.

I like this paper because it is one of the first explorations of what it means to use limb-darkening laws to model the intensity profile of a star, that is the change of the amount of light emitted from the centre of a stellar disk to the edge. We find that limb-darkening depends on how you model stellar atmospheres and that the laws contain information about the radiation of the star. Limb-darkening is shown in the plot below,


where μ=1 is the centre of a stellar disk and μ=0 is the edge and I is the intensity of light. The black lines refer to limb-darkening from an observed star (Fields et al. 2003, ApJ, 596, 1305) and the blue and red lines are limb-darkening laws from two different types of model stellar atmospheres. The blue lines are for plane-parallel model atmospheres, which assumes that the stellar atmosphere is infinitesimally thin relative to the size of the star, and the red lines are for spherically symmetric stellar atmospheres which do not make this assumption.
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The Cepheid mass discrepancy and pulsation-driven mass loss

Just had a letter accepted for publication in Astronomy & Astrophysics titled “The Cepheid mass discrepancy and pulsation-driven mass loss” co-authored with Dr. Matteo Cantiello and Prof. Norbert Langer from the Argelander Institute for Astronomy. The abstract is

Context. A longstanding challenge for understanding classical Cepheids is the Cepheid mass discrepancy, where theoretical mass estimates using stellar evolution and stellar pulsation calculations have been found to differ by approximately 10 - 20%. Aims. We study the role of pulsation-driven mass loss during the Cepheid stage of evolution as a possible solution to this mass discrepancy.
Methods. We computed stellar evolution models with a Cepheid mass-loss prescription and various amounts of convective core overshooting. The contribution of mass loss towards the mass discrepancy is determined using these models, Results. Pulsation-driven mass loss is found to trap Cepheid evolution on the instability strip, allowing them to lose about 5 10% of their total mass when moderate convective core overshooting, an amount consistent with observations of other stars, is included in the stellar models.
Conclusions. We find that the combination of moderate convective core overshooting and pulsation-driven mass loss can solve the Cepheid mass discrepancy.

In this work, we are trying to understand an important problem in the understanding of the variable star Cepheids and stellar physics, in general, called the “Cepheid mass discrepancy”, which deserved a post all its own. A quick definition of the problem is that there are two ways of measuring the masses of these stars. One is modeling how the star evolves and matching the observed properties of the star and getting a mass from the best-fit models, what we call the stellar evolution mass. The second method is modeling the change of brightness and radius of a Cepheid due to stellar pulsation and matching the observed period and brightness changes to get a mass, called stellar pulsation masses. The problem is these methods do not agree and stellar evolution masses are about 20% greater than the stellar pulsation masses.

This might not sound like a big difference, but it is enough to challenge our understanding of stellar physics. In our paper, we test how a stellar wind generated by the pulsation of a Cepheid can help solve the discrepancy by adding a mass loss theory to stellar evolution models of Cepheids. We find winds on their own won’t solve the discrepancy so we include some added physics to find agreement. The predicted mass discrepancy for some of our models is
where we find our predicted mass discrepancy agrees with other measurements suggesting that a Cepheid wind plays an important role in resolving the Cepheid mass discrepancy.
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