Astroplots

Vignettes in astrophysical data representation

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If you’ve been closely following the latest research on extrasolar planets on Astrobites, you might wonder why so much discussion is focused on the sizes or radii of planets.  After all, what we’re really looking for in the search for Earth-like planets are exoplanets with compositions similar to Earth.  Big is fine, as long as it’s rocky and not gaseous!  New results published by Howard et al. point to what may be the most Earth-like extrasolar planet yet discovered, with respect to composition.
At issue is the Kepler spacecraft, which has provided astronomers with a bonanza of extrasolar planet discoveries.  Kepler assesses planets’ radii at the same time it discovers them, by measuring the fraction of light blocked by the planet as it transits in front of its parent star.  To measure mass, we instead need very high resolution spectroscopy of the star to watch as it wobbles in its orbit with the planet via the Doppler effect.  
Howard et al. used this technique to measure the mass of planet Kepler-78b - what they found is a planet which is likely (see the gray probability distribution and red 1σ uncertainty ellipse) just a little bigger and more massive than Earth and Venus (green triangles).  That makes it the lowest mass of all exoplanets (red circles) ever found to be consistent with a rocky density (lines trace theoretical models)!  Future observations that fill in this plot with more exoplanets will allow us to explore the full diversity of planetary compositions in the universe.

If you’ve been closely following the latest research on extrasolar planets on Astrobites, you might wonder why so much discussion is focused on the sizes or radii of planets.  After all, what we’re really looking for in the search for Earth-like planets are exoplanets with compositions similar to Earth.  Big is fine, as long as it’s rocky and not gaseous!  New results published by Howard et al. point to what may be the most Earth-like extrasolar planet yet discovered, with respect to composition.

At issue is the Kepler spacecraft, which has provided astronomers with a bonanza of extrasolar planet discoveries.  Kepler assesses planets’ radii at the same time it discovers them, by measuring the fraction of light blocked by the planet as it transits in front of its parent star.  To measure mass, we instead need very high resolution spectroscopy of the star to watch as it wobbles in its orbit with the planet via the Doppler effect.  

Howard et al. used this technique to measure the mass of planet Kepler-78b - what they found is a planet which is likely (see the gray probability distribution and red 1σ uncertainty ellipse) just a little bigger and more massive than Earth and Venus (green triangles).  That makes it the lowest mass of all exoplanets (red circles) ever found to be consistent with a rocky density (lines trace theoretical models)!  Future observations that fill in this plot with more exoplanets will allow us to explore the full diversity of planetary compositions in the universe.

Filed under Kepler planets spectroscopy

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You’re looking at the first map ever made of a planet around another star.  Of course, even the next generation of astronomical instrumentation is orders of magnitude away from achieving the resolution needed to actually produce an image of a planet that far away.  But Knutson et al. (2007) took a different approach - they let the planet resolve itself.  Using the Spitzer Space Telescope, they took about 300,000 consecutive images of the star HD 189733 as its primary planet (a Hot Jupiter) slowly completed its orbit.  With each image, the planet slowly rotated before the camera.  They then calculated the brightness of the star+planet system as a function of the planet’s rotation angle (longitude), shown in part b) of the figure above.  With that information, they constructed a map of the brightness distribution on the planet surface (part a).  This map provided some of the most valuable constraints to date on the temperature variation across a planet’s surface from day to night, and has led to important consequences in our understanding of the atmospheres of Hot Jupiters.

You’re looking at the first map ever made of a planet around another star.  Of course, even the next generation of astronomical instrumentation is orders of magnitude away from achieving the resolution needed to actually produce an image of a planet that far away.  But Knutson et al. (2007) took a different approach - they let the planet resolve itself.  Using the Spitzer Space Telescope, they took about 300,000 consecutive images of the star HD 189733 as its primary planet (a Hot Jupiter) slowly completed its orbit.  With each image, the planet slowly rotated before the camera.  They then calculated the brightness of the star+planet system as a function of the planet’s rotation angle (longitude), shown in part b) of the figure above.  With that information, they constructed a map of the brightness distribution on the planet surface (part a).  This map provided some of the most valuable constraints to date on the temperature variation across a planet’s surface from day to night, and has led to important consequences in our understanding of the atmospheres of Hot Jupiters.

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Take a look at the top plot.  It shows how many stars can be found in hypothetical boxes of space at positions z above or below the sun, and at longitudinal angles l within the Galactic disk.  Do you see anything amiss?

If you stare very closely, you may find that the distribution is not symmetric.  There is an overabundance of stars (hot spots) just below the sun, and an under-abundance (cool spots) above it.  

Yanny & Gardner took a better approach than staring - they compared the number density measurements to a symmetric model and found a wave-like pattern in the residuals.  The bottom plot literally shows this ripple in the distribution of stars in the Milky Way.

But what causes this wave-shaped asymmetry?  Perhaps it is the gravitational signature of an encounter our galaxy had long ago with a disruptive satellite galaxy.

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This type of plot is common in papers describing theoretical models of supernovae and other stellar explosions.  It is a graphical representation of the nucleosynthesis which occurs in the ejected material.  This specific plot is from Shen et al. (2010) and represents the detonation of a 0.2 solar mass helium shell on the surface of a 0.6 solar mass white dwarf.
The x-axis is presented in terms of the “mass enclosed”.  This is a proxy for radius and is precisely what it sounds like: the amount of mass which is inside a certain location.  For this particular model 0.6 is base of the (initially) helium shell and 0.8 is the outer edge.  The y-axis is the mass fraction, with 1.0 representing all of the mass at a certain radius.  Each colored line therefore tells you what fraction of the mass at a certain radius is made up of that element.  For example, at a mass enclosed of ~0.66 Msun, 80% of the material has been burned to Nickel (black line).
You can see in this particular model, most of the inner part of the shell was burned to iron peak elements (titanium, chromium , iron, nickel), while in the outer part of the shell over half of the mass is still unburned helium.

This type of plot is common in papers describing theoretical models of supernovae and other stellar explosions.  It is a graphical representation of the nucleosynthesis which occurs in the ejected material.  This specific plot is from Shen et al. (2010) and represents the detonation of a 0.2 solar mass helium shell on the surface of a 0.6 solar mass white dwarf.

The x-axis is presented in terms of the “mass enclosed”.  This is a proxy for radius and is precisely what it sounds like: the amount of mass which is inside a certain location.  For this particular model 0.6 is base of the (initially) helium shell and 0.8 is the outer edge.  The y-axis is the mass fraction, with 1.0 representing all of the mass at a certain radius.  Each colored line therefore tells you what fraction of the mass at a certain radius is made up of that element.  For example, at a mass enclosed of ~0.66 Msun, 80% of the material has been burned to Nickel (black line).

You can see in this particular model, most of the inner part of the shell was burned to iron peak elements (titanium, chromium , iron, nickel), while in the outer part of the shell over half of the mass is still unburned helium.

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Understanding how galaxies convert gas into stars is one of the hottest topics in astrophysics at the moment. Since denser gas tends to collapse more quickly, one would expect that regions of galaxies known to host dense gas will tend to form stars more quickly. This was originally pointed out by Schmidt in the 50’s and was later taken up by Rob Kennicutt in the late 90’s. The plot above is a representation of what is known as the “Kennicutt-Schmidt Law”.
This isn’t a law in the sense of Newton’s law of gravity, but more of an empirical relation found to hold true in a galaxies wherever we measure it. The law is the relationship between the surface density of gas and the surface density of star formation, measured either in local patches of a galaxy or over entire galaxies where a local measurement isn’t feasible. The plot above was originally published by Frank Bigiel and the THINGS team using data from the VLA, GALEX, and the Spitzer Space Telescope as well as a large number of datasets taken from the literature, as indicated on the plot. The colored contours are Bigiel’s dataset and correspond to local measurements in nearby galaxies. The points are literature values and correspond to whole regions of galaxies.
The structure in this plot tells us about the physics of star formation. For example, the abrupt change in the slope of the relation at a gas surface density of 10 solar masses per square parsec (the left-hand vertical dotted line) corresponds to a phase transition at the surface density when atomic hydrogen gas recombines to form molecular hydrogen.

Understanding how galaxies convert gas into stars is one of the hottest topics in astrophysics at the moment. Since denser gas tends to collapse more quickly, one would expect that regions of galaxies known to host dense gas will tend to form stars more quickly. This was originally pointed out by Schmidt in the 50’s and was later taken up by Rob Kennicutt in the late 90’s. The plot above is a representation of what is known as the “Kennicutt-Schmidt Law”.

This isn’t a law in the sense of Newton’s law of gravity, but more of an empirical relation found to hold true in a galaxies wherever we measure it. The law is the relationship between the surface density of gas and the surface density of star formation, measured either in local patches of a galaxy or over entire galaxies where a local measurement isn’t feasible. The plot above was originally published by Frank Bigiel and the THINGS team using data from the VLA, GALEX, and the Spitzer Space Telescope as well as a large number of datasets taken from the literature, as indicated on the plot. The colored contours are Bigiel’s dataset and correspond to local measurements in nearby galaxies. The points are literature values and correspond to whole regions of galaxies.

The structure in this plot tells us about the physics of star formation. For example, the abrupt change in the slope of the relation at a gas surface density of 10 solar masses per square parsec (the left-hand vertical dotted line) corresponds to a phase transition at the surface density when atomic hydrogen gas recombines to form molecular hydrogen.

Filed under Star formation

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The data in this plot is fake, but the analysis is fantastic.  Fitting a line to data, or linear regression, is often considered a simple task in practice.  But in theory, things are much more complicated.
Hogg et al. (2010) describes best practices for comparing models with data, and making inferences on the parameters of the model.  They discuss all the caveats which are easy to ignore — uncertainties along both axes, intrinsic variation within the model, and how to properly account for outlier points — in the context of both Bayesian and frequentist points of view.  In this plot (Figure 13 of the paper), they show the confidence interval for the best-fit relation between the points (dashed lines) while taking into account the covariate uncertainties (ellipses) and intrinsic scatter.

The data in this plot is fake, but the analysis is fantastic.  Fitting a line to data, or linear regression, is often considered a simple task in practice.  But in theory, things are much more complicated.

Hogg et al. (2010) describes best practices for comparing models with data, and making inferences on the parameters of the model.  They discuss all the caveats which are easy to ignore — uncertainties along both axes, intrinsic variation within the model, and how to properly account for outlier points — in the context of both Bayesian and frequentist points of view.  In this plot (Figure 13 of the paper), they show the confidence interval for the best-fit relation between the points (dashed lines) while taking into account the covariate uncertainties (ellipses) and intrinsic scatter.

Filed under statistics

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The orbital decay of a binary pulsar. The first binary pulsar was detected by Hulse and Taylor in 1975.  Over the subsequent years, the orbital period of the pulsar pair was carefully measured, producing the figure above which was published by Taylor and Weisberg in 1981.  The flat line corresponds to an unchanging orbital period, while the solid black line corresponds to the general relativistic prediction for the decay in the orbital period due to the emission of gravitational radiation.  So far, this is the only observational confirmation of gravitational radiation.  Hulse and Taylor were awarded the Nobel Prize in 1993 for their discovery.

The orbital decay of a binary pulsar. The first binary pulsar was detected by Hulse and Taylor in 1975.  Over the subsequent years, the orbital period of the pulsar pair was carefully measured, producing the figure above which was published by Taylor and Weisberg in 1981.  The flat line corresponds to an unchanging orbital period, while the solid black line corresponds to the general relativistic prediction for the decay in the orbital period due to the emission of gravitational radiation.  So far, this is the only observational confirmation of gravitational radiation.  Hulse and Taylor were awarded the Nobel Prize in 1993 for their discovery.

Filed under gravitational waves pulsar

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This plot is a representation of some of the results from the latest Millennium Simulation (reference: Lemson et al. 2006. image credit: MPA-Garching).  Each point on this plot represents a galaxy. Within each piece slice, distance from the center represents redshift, or distance, while placement around the circle represents direction.  The blue and purple points are real galaxies. They show that the galaxies of the universe are not uniformly distributed but rather form filaments, clumps, and voids.  The red points are simulated galaxies.  The Millennium Simulation took 10 billion particles, placed them in an initial configuration, and let them evolve forward according the rules of lambda-CDM cosmology (lambda = the cosmological constant = dark energy. CDM = cold dark matter). This shows that the simulation is capable of closely mimicking the observed large scale structure of the universe.

This plot is a representation of some of the results from the latest Millennium Simulation (reference: Lemson et al. 2006. image credit: MPA-Garching).  Each point on this plot represents a galaxy. Within each piece slice, distance from the center represents redshift, or distance, while placement around the circle represents direction.  The blue and purple points are real galaxies. They show that the galaxies of the universe are not uniformly distributed but rather form filaments, clumps, and voids.  The red points are simulated galaxies.  The Millennium Simulation took 10 billion particles, placed them in an initial configuration, and let them evolve forward according the rules of lambda-CDM cosmology (lambda = the cosmological constant = dark energy. CDM = cold dark matter). This shows that the simulation is capable of closely mimicking the observed large scale structure of the universe.

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This is the original plot which showed what is now called the Phillips Relation for Type Ia supernovae (reference: Phillips et al. 1993). Each point is an individual supernova. The vertical axis shows the peak absolute magnitude of these supernovae while the horizontal axis shows a parameter called delta M15.  Delta M15 is the number of magnitudes a supernovae fades in the first 15 days after maximum.  A large Delta M15 implies the supernovae decays quickly.  You can see that not all of the Type Ia supernovae have the same peak magnitude.  However, there is a linear relationship between peak magnitude and delta M15 (which has since been confirmed by hundreds of additional supernovae).  Phillips realized this meant that Type Ia supernovae could be corrected to the same magnitude as long as their decline rate was known.  This makes them standardizable candles.  
The discovery that Type Ia supernovae could be standardized in this way is what allowed the measurements which eventually lead to the discovery that the expansion of the universe was accelerating (i.e. dark energy).  This, in turn, was awarded the 2011 Nobel prize in physics.

This is the original plot which showed what is now called the Phillips Relation for Type Ia supernovae (reference: Phillips et al. 1993). Each point is an individual supernova. The vertical axis shows the peak absolute magnitude of these supernovae while the horizontal axis shows a parameter called delta M15.  Delta M15 is the number of magnitudes a supernovae fades in the first 15 days after maximum.  A large Delta M15 implies the supernovae decays quickly.  You can see that not all of the Type Ia supernovae have the same peak magnitude.  However, there is a linear relationship between peak magnitude and delta M15 (which has since been confirmed by hundreds of additional supernovae).  Phillips realized this meant that Type Ia supernovae could be corrected to the same magnitude as long as their decline rate was known.  This makes them standardizable candles.  

The discovery that Type Ia supernovae could be standardized in this way is what allowed the measurements which eventually lead to the discovery that the expansion of the universe was accelerating (i.e. dark energy).  This, in turn, was awarded the 2011 Nobel prize in physics.

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The Salpeter slope of the initial mass function. The initial mass function (or IMF for short - not to be confused with the other IMF) measures the number of stars that form at a given stellar mass.  Said another way, if I know the IMF, I can tell you how many one solar mass stars form for every 10 solar mass star.  Knowing the IMF is key since the brightest stars dominate the starlight we see, yet the mass of stars is dominated by comparably invisibly dim stars with masses similar to the sun.
Salpeter’s measurement (Salpeter 1955) is presented above as the solid black line.  The x axis is the stellar mass, in units of solar masses, presented on a log scale.  Perhaps a bit confusingly, stars with masses larger than the sun are on the left-hand side, and stars with masses smaller than the sun are on the right-hand side.  The scale at the top of plot shows the same information, but plots the star’s absolute magnitude (i.e. how bright the star is) instead of the star’s mass.  On the y-axis is the IMF, for which Salpeter used the symbol ξ.  The units for ξ(m) are somewhat arbitrary, since it corresponds to the relative probability of finding a star at any given mass.  The black line can be well fit be a power law that scales as the stellar mass to the minus 1.35 power.  This power-law slope is known at the Salpeter slope of the IMF. The paper this figure was published in currently has more than 4000 citations and is among the most cited papers in the astrophysical literature.

The Salpeter slope of the initial mass function. The initial mass function (or IMF for short - not to be confused with the other IMF) measures the number of stars that form at a given stellar mass.  Said another way, if I know the IMF, I can tell you how many one solar mass stars form for every 10 solar mass star.  Knowing the IMF is key since the brightest stars dominate the starlight we see, yet the mass of stars is dominated by comparably invisibly dim stars with masses similar to the sun.

Salpeter’s measurement (Salpeter 1955) is presented above as the solid black line.  The x axis is the stellar mass, in units of solar masses, presented on a log scale.  Perhaps a bit confusingly, stars with masses larger than the sun are on the left-hand side, and stars with masses smaller than the sun are on the right-hand side.  The scale at the top of plot shows the same information, but plots the star’s absolute magnitude (i.e. how bright the star is) instead of the star’s mass.  On the y-axis is the IMF, for which Salpeter used the symbol ξ.  The units for ξ(m) are somewhat arbitrary, since it corresponds to the relative probability of finding a star at any given mass.  The black line can be well fit be a power law that scales as the stellar mass to the minus 1.35 power.  This power-law slope is known at the Salpeter slope of the IMF. The paper this figure was published in currently has more than 4000 citations and is among the most cited papers in the astrophysical literature.

Filed under star formation