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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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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Pulsating Stars Under the Spanish Sun

I just returned from a conference in Granada Spain on Stellar Pulsation, I took some pictures that you can see here. The conference was very interesting, discussing almost all aspects of pulsating variable stars, the city was amazing, with clear skies and 30 degree heat and no, absolutely no humidity. The only problem was getting there.

So, I’ll start with the rant. I have flown a number of different airlines, but this had to be the worst experience ever. In case you are wondering, the airline is Iberia. My flight plan for this conference was to fly from Frankfurt to Madrid, have a one hour wait and then connect to Granada. That sounds easy enough, but somehow it isn’t. The first problem is that we appear to board the plane on time but for no apparent reason the flight didn’t take off for another half hour. That would be fine, I would still have a half hour to make my connection, the exception being that my seat in the plane had only enough space to accommodate small children. I had one leg resting in the pathway, tripping the flight attendants as they walked by ignoring everyone and the other leg bent in a shape that only a professional contortionist could envy. Fine, I can survive that. While in the air, the attendants have a snack service where they charge for everything, even two euros for a cup of bad coffee. Fine, it is only a short flight, I can wait. I mean, I had a short connection and would be in Granada in only a few hours.

No, that wasn’t going to happen. Somehow, the flight took longer than scheduled and I ran as fast as I could to make the connection, getting there just in time, but the gate was closed. No dice. So I go to the service desk to reschedule. They tell me I cannot get the next flight to Granada and have to wait 8 hours fine. They compensate me with a meal voucher for the cafeteria. That sounds alright, no, people behind in the service line were put on the next flight, I was just screwed over, and the food... well I am being generous in calling it food. I had meatballs that smelled and looked like dog food, with cheap boiled vegetables. That was crap.

Fine, fine. I make my connection and again it is late leaving. My 5 hour trip turned in 15 hours, I might have been able to drive to Granada in 15 hours. But fine, I made it... time to move on, stupid Iberia.

The conference was interesting with a lot of discussion about Cepheids and RR Lyrae Stars, and asteroseismology with the Kepler and CoRot satellites. I learned a fair bit about the Blazkho effect, a phenomenon known for about a century but there was no clue about the source of the phenomenon until recently, thanks to Kepler. Hear that NASA, your space observatories are awesome. Maybe, I’ll write more about the conference and the astrophysics later. At the moment, I am more interested in Granada, and in particular the Alhambra.

The Alhambra or Red Fortress is an old city build by early Islamic settlers in Spain when they were establishing a Caliphate. Over time, Christians took over the Alhambra and attempted to change the old city and make it more christian. Later on, the Spanish built new palaces in honour of the Habsburg emperor. There is now a mix of relics and ruins and more recent unfinished palaces and a mix of medieval and modern history.


From the outside, it is obvious how the Alhambra earned its name. It is a massive structure on a hill overlooking much of Granada. However, the most amazing part of the Alhambra is not the outside or the scale of the buildings but the detailed designs decorating the interior throughout. There are archways and ceilings designed to look like there are stalagmites hanging, giving the visitor the impression that they are in a natural shelter and not a man-made one. More so, my eyes pulled towards the intricate geometric designs painted on walls throughout the complex. It is interesting how precise these designs are. I could only stand there awestruck when I imagined the number of artisans patiently and carefully painting the walls for many and many days.


Further along, there are many more designs, patterns etched in the walls. They intricate, geometric patterns with no apparent differences from on part of the wall to another, made of perfect circles and intertwined lines, repeating across the room, like modern, industrial tiles but done by hand. The arches have similar designs, with smaller arches gently carved with the larger.


However, I think my favourite design is in the pictures below, shown in two different ways. The design appears to be of the Sun, blazing in the sky, with a perfect symmetry of light rays from the Sun. The iconography presented in the Alhambra embraces nature and the sky, with a detailed precision and repetition that I have never seen. I am fortunate to have seen this human achievement up close, because it is something that will be reproduced again because of industrial manufacturing and costs of doing such work by hand.

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Naples and the Distance to Everything

After I returned to Germany from China, I turned right back around and hopped on a plane to Naples for a conference on the Cosmic Distance Scale. The goal of this conference was to understand how well astronomers can measure the distances to far away stellar objects and galaxies and use this information to measure the rate of expansion of the universe, denoted by Hubble’s Constant H0. By more precisely measuring the expansion, it is hoped that we can better understand the structure of the universe, and the physics of the universe such as dark energy.

I contributed a small poster focusing on the details of Cepheids, how they lose mass in winds, and how this mass loss contributes to the amount of infrared light (light at wavelengths longer than that which can be seen by people). Cepheids are important distance indicators because they pulsate. The amount of light a Cepheid emits varies over a few - 100 days and repeats over and over again, and the period of this variation tells us how much light this is, not just the amount of light we see. Thus, with this information we can measure the distances to these stars and to the galaxies that we see Cepheids in. However, they are not perfect distance indicators, the relation between the amount of light emitted and the period of variation also depends on what a Cepheid is composed of. For example, the Sun is about 70% hydrogen, 28% helium, and 2% everything else and Cepheids is our galaxy have very similar compositions. In another galaxy though a Cepheid that emits the exact same amount of light as our Galactic Cepheid may have composition 73%, 26% helium and 1%, but the period of variation will be different. This means we would predict a wrong distance to that galaxy, and means we have an uncertainty in measuring distance and H0.

In infrared light, it is believed that this uncertainty due to composition decreases and thus one can measure distances more precisely. For my poster, I showed that Cepheids have winds that generate an infrared excess due to dust forming around the Cepheid. The amount of dust and hence amount of extra infrared light depends on the composition of the Cepheid and means that the brightness we see is larger than it would be if there were no dust. Since we don’t know how much dust may be around a Cepheid in another galaxy then there is an extra uncertainty in measuring distances that is not understood. It was not the most positive message for measuring cosmic distances but is interesting for understanding how these stars evolve.

There were some very interesting talks, discussing a wide variety of objects for measuring distances. There were talks on supernovae, planetary nebulae, RR Lyrae stars, and more. The talk on supernovae was interesting in that the researchers used Cepheids to calibrate the distance to nearby explosions of white dwarf stars. An exploding white dwarf emits almost the exact same amount of light as every other exploding white dwarf, (though there are exceptions) which makes it another very powerful distance indicator, and you can see further way than almost every other distance indicator. Using these stars, the researcher and his team determined one of the most precise values of the Hubble Constant ever, it is almost precise enough to constrain other aspects of cosmology, such as the amount of matter in the universe.

One lesson I took from the conference is that these great results depend on who and how the observations are treated. Using the same Cepheids, different researchers found a very different value of the Hubble Constant. This tells me that astronomers must be very careful and there needs to be multiple tests to understand measurements like the Hubble Constant and we need to be careful in taking these great measurements and announcements too seriously. The results may easily change.

Beyond the conference, Naples was an interesting city. There was a dramatic juxtaposition between the amazing view of the Mediterranean Sea and surrounding mountains and views of garbage piling up on street sides and building looking old and run down. This was a little disappointing but the food, the food, more than made up for it. The food in Naples was amazing. However, the highlight of the trip was a visit to Pompeii, which is worth the trip all on its own. I’ll talk about that in a future post.
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Stellar Astrophysics in Lijiang

I returned a week or so ago from a couple of conferences, one in Lijiang, China, and one in Naples, Italy. I’ll write about the latter conference in a later post. The conference in Lijiang was titled The 9th Pacific Rim Conference on Stellar Astrophysics and featured a number of presentations and posters on various aspects of stellar astronomy from star formation to Cepheids to black holes. This conference was also interesting because it coincided with an international summer school organized by the International Astronomical Union.

In the conference, I spoke about the star Betelgeuse and a new method to measure its mass based on observing the change in the amount of light from the center of the stellar disk to the edge. This is because the change of light depends on the structure of the outer layers of the star, and more important on what fraction of the stellar radius is the depth of the atmosphere. If we can measure this atmospheric extension then we can measure the mass of star. I applied the method to observations of Betelgeuse to determine its mass. I gave a second talk on the Cepheid mass discrepancy, see my earlier post. In this talk, I discussed if winds could explain the mass discrepancy for Cepheids in our galaxy and the discrepancy of Cepheids in the Large Magellanic Cloud. I found that winds can explain the result for Galactic Cepheids but was inconclusive for the Magellanic Cloud Cepheids. Still more work to be done.

Other talks were much more interesting. There was a talk showing that the Earth and Sun currently in the middle of a bubble in the interstellar medium where there is less gas. The bubble was created by supernovae that exploded a long time ago. Another talk discussed the habitability of planets orbiting a very low mass, cool star called an M dwarf. This is important because these stars are among the most common in the universe and therefore most extrasolar planets are likely to orbit these stars. One of my favorite was an talk discussing observations of a type of binary stars called Algols, where the speaker showed a plot suggesting that in these systems the binaries will merge and form one star. It was a bit of a subtle plot but very cool.

The most interesting part of the conference was meeting the students from the summer school. These students came from many different parts of Asia, including Vietnam, Nepal, and even North Korea. It was a unique opportunity to learn about these cultures and astronomy in their home countries. I really liked the meeting and look forward to the 10th Pacific Rim Meeting on Stellar Astrophysics.
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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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