Lecture Notes of Stellar Astrophysics PDF

LECTURE NOTES OF STELLAR ASTROPHYSICS PROF. ANTONINO MILONE These notes refer to the academic year 2021-2022 - Lara Senter Lecture 1 - READING THE COLOR-MAGNITUDE DIAGRAM CMD is one of the main tools to understand the properties of stars from o...

LECTURE NOTES OF STELLAR ASTROPHYSICS PROF. ANTONINO MILONE These notes refer to the academic year 2021-2022 - Lara Senter Lecture 1 - READING THE COLOR-MAGNITUDE DIAGRAM CMD is one of the main tools to understand the properties of stars from observations. Resolved stellar population – resolved stars Resolved stellar population is a concept that depends on the observational tool that we have, so if we use high resolution telescope. Resolved stelar population is a population of stars where we can distinguish one star to another. We can measure the luminosity of single stars (the technique is photometry) and we can infer the chemical composition and detailed chemical abundances of single stars (e.g., from the spectra). With the spectrograph we can get the lines, and from the lines and molecular bands, we can infer the chemical composition of the stars. Unresolved stellar population We cannot resolve the light of single stars. To get info on galaxies we need to use integrated light. We can obtain integrated luminosity or integrated spectra. In the distance universe we cannot get information of unresolved stellar population unless we know the properties of stellar population from resolved stars. We need to understand the stars to understand the distance universe. Properties from resolved photometry and spectroscopy to understand the integrated properties of light from distance Gs. Reminder LUMINOSITY (L): it is an intrinsic property of an object. It is the total amount of electromagnetic energy emitted by a star per unit time [unit J/s, W ]. Luminosity is different from the observed flux/apparent brightness of the stellar source. OBSERVED FLUX (or APPARENT BRIGHTNESS): F, is the power per unit area that we receive from a star [unit W/m2]. It depends on distance, d, and diminishes as the inverse square of the distance → F = L / 4πd2 APPARENT MAGNITUDE: logarithmic measurement of the apparent brightness. Apparent magnitude is NOT Luminosity! A star can exhibit faint (high) apparent magnitude because it is far from us, or because its luminosity is low. Simple stellar population – SSP A simple stellar population is the assembly of stars that have the same age and the same chemical composition. A SSP is described by four main parameters: 1. age 2. chemical composition (Y, Z). We refer it to the content of three elements: hydrogen, helium (Y) and metals (Z). 3. initial mass function (IMF). It is the number of stars per interval of mass after the formation of the stellar population. It is very important for the history of the universe, and it is difficult to derive because if we observe a globular cluster formed at a very high redshift we do not observe the IMF but the present day function, that if the IMF after 13 Gyr of stellar and dynamical evolution. It is really challenging to reconstruct the IMF starting from the present-day mass function. Stars of a SSP are coeval, which means that they formed in a single star formation burst. Moreover they are chemically homogeneous, that is all stars are born with the same chemical composition. Complex stellar population The opposite of SSP is multiple/complex stellar population CSP. When one or more of the properties of SSP are not fulfilled, the stellar population under scrutiny is a complex stellar population and it is composed by various SSPs. When studying stellar systems we try to split the complex stellar system into a collection of SSPs. Globular Clusters Some candidates of SSP are globular clusters. They were considered to be the best examples of old SSPs in nature. They are the ancient stellar system. For the first half of the course we will consider globular clusters (GC) as SSPs. GC are used as example of stella population to infer the properties of the stars and SSP. They are populated by up to millions of old stars. GC are spherical objects present mostly in halo of Milky Way, but they also populate the internal part of the galaxy: the bulge, and they are also present in the galactic disk. Their stars are very tightly bound by gravity, which gives them their spherical shapes and relatively high stellar densities toward their centres. They are old and have relatively low mass and the density, which depends on the radial distance, increases towards the centre. Young stellar population It is an alternative to GC. Historically, open clusters were considered the best examples of young SSPs in nature. The GC of the Milky Way are old systems, they have ages older than 12 Gyrs. Instead, open clusters are young SSP in nature. You can find them surrounded by a cloud that formed the cluster itself. Open clusters, in contrary to GC, are a collection of small number of stars. Group of up to a few thousand stars weakly gravitationally bound that were formed by the same molecular cloud. They usually populate the disk of the galaxy, so they have lot of interaction with the main value of the galaxy. Open clusters are often populated by young stars. Since they are weakly gravitationally bounded with each other, they can dissolve after few hundreds Myr depending on the mass, density and other parameters. 1 Stellar population I and II There is not a sharp definition between open clusters and globular clusters. GLOBULAR CLUSTER OPEN CLUSTER Old Young Host population II stars (old metal poor stars) Host population I stars (young metal rich stars) Population III stars have never been discovered and they do not contain any metal (elements heavier then Helium). They have the same chemical composition of the material after the big bang, so a high content of hydrogen and helium and a tiny amount of Lithium. The picture on the left shows a simplification of the structure of our galaxy. When we approach the disk of the galaxy (in blue), we have extreme (very young and they are forming now) population I. Moving at higher galactic latitude we have a mix of population I very young stars and an intermediate of population I stars. Then we have a transition from population I to population II. In the halo nearly all the stars are metal poor stars so population II stars. Star in a clusters 1. have different colors depending on their temperature. Some stars look reddish, bluer, whiter. 2. have different luminosities, dimensions. 3. share the same distance. They are located at the same distance and so the apparent brightness corresponds to the intrinsic luminosity. But remember that apparent magnitude is NOT luminosity. But when we are in a star cluster, all the stars have the same distance, and we can consider the apparent magnitude as the intrinsic one. The Color-Magnitude diagram – CMD The color-magnitude diagram (CMD) is a plot of the star’s magnitude (which is indicative of the stellar luminosity) as a function of the color of the star (which is a proxy of the temperature). The color of a star is a difference of two magnitudes, blue means hot and red means cold. The CMD is an observer’s diagram. The sequence in which the stars are located is closely connected with the evolution of the stars. On the left you observe the CMD of an old cluster. Whereas on the right you have the CMD of a young cluster. In the case of a young cluster is more difficult to see which stars belong to the cluster and which ones belong to the external field. When observing an open cluster, it is usually close to us and in the direction of the galactic disk so there are a lot of stars not cluster members. The challenge is to understand which stars belong to the cluster, so that we can conclude that they have the same age, chemical composition and distances. The stars not belonging to the cluster are useless. Now that we have GAIA we do that for close clusters using proper motion because stars in a cluster have a common motion in the plane of the sky together with the radial velocity that provide the velocity of the stars along the line of sight. Stars withing a cluster have random motion but considering the hole cluster they have a common motion. Magellanic clouds: there are families of cluster very interesting. Statistic decontamination is used for cluster located far away, for example clusters in the Magellanic cloud. They observe a field that is centred in the cloud and the reference field does not include the stars cluster because it is a bit farther away than the centre of the cluster. But it has the same properties because it is nearby and the distribution of the filed stars is the same in the cluster field and reference field, and what they do is to decontaminate stars from the field. Investigating near by cluster we use GAIA, instead for far away cluster we use stellar proper motion. Looking at proper motion we can separate members of different field stars. Stars in the cluster have different motion with respect to the cluster in the surrounding field. To quantify it we make the vector-point diagram of proper motion (on the right). On the x axis we have the motion in the direction of the right ascension and on the y axis we have the direction in the direction of the declination. We see that stars are not distributed randomly but they form two main blobs of stars, one where the velocity dispersion is small and the other for which the velocity dispersion is very high. From the CMD you are not able to disentangle cluster and field stars. Instead, it is clear which stars belong to the cluster using the proper motion diagram. Thanks to that we can then distinguish the CMD of different star clusters and studying the stellar evolution. 2 How do we construct the CMD? Observationally, we solve stars in colors and then we solve stars in luminosities, in such a way that bright stars are in the upper part of the CMD and the faint stars are in the bottom of CMD. Stars in a cluster follow sequences, and each sequence is indicative of the properties of star itself. Each point in the diagram on the left is indicative of the evolutionary phase of a star. MAIN SEQUENCE STARS: stars that are similarly to the Sun burning hydrogen in the core. It is the way they produce their luminosity. SUB GIANT BRANCH: evolving in the red giant branch phase where we have different processes responsible for the luminosity of the star. HORIZONTAL BRANCH: the stars are producing energy not burning hydrogen but burning helium. WHITE DWARF COOLING SEQUENCE OF STARS: the luminosity is not produced by nuclear reaction but by different phenomena. By looking at the CMD we can get which star belong to which evolutionary sequence, but we can get more info. We can understand the age of the stellar population. For young clusters the CMD has a very blue turn off point for which stars move to the red. If cluster gets older the turn off point gets fainter and redder. With the CMD we can also infer the presence of binary stars, the presence of multiple stellar population, chemical composition of single star (and then star formation history of stellar system), information about the primordial cloud that originated the cluster at high redshift, evolution. The turn off is a clock to establish the age of the stellar population. The turn off tells when stars finished the hydrogen in the core. You start to burn hydrogen in the shell. Star clusters are used to infer age at high precision, and it is done using the turn off point. Different parts of the diagram are sensitive with different aspect of the evolution. Lecture 2 - READING THE COLOR MAGNITUDE DIAGRAM Summary CMD: very powerful tool to investigate the properties of stars and the properties of stellar populations. Light is produced by stars and so information from distant universe comes from stars. They are the building block of the galaxies, the units of the universe. Most stars form in clusters, so it is why we are interested in clusters. A simple stellar population (SSP) is a group of stars that formed from the same primordial cloud. So what we have is a primordial cloud, the gas of the cloud is mixed and so it is chemically homogeneous. From this gas we have the formation of stars. All stars of the same population have common properties: same age, same chemical composition (Y, Z), same initial mass function (number of stars per unit of mass). In the reference frame of the stellar system the stars have random motion with respect to the other. But in the reference frame of the host galaxy, the stars have a common motion, so it is possible to recognize them. SSP are important, because when we study complex stellar population, like galaxies or globular cluster, we consider them as collection of SSP. Young SSP are the open cluster. Whereas the old SSP are globular cluster. Both GC and OC are complex stellar systems, in a sense more complex than a galaxy. It is not so clear what an OC and a GC is. Form the picture on the right we may say they are an OC and a GC, but in reality from definition they are both OC. Historically, open clusters were considered the best examples of young SSPs in nature. Remember that stars in a cluster share the same distance. So, the difference in luminosity that is observed in stars that belong to a cluster is intrinsic luminosity. Whereas if I look at stars in the sky is difficult to determine whether the luminosity is apparent or intrinsic. This because we don’t know the distance. To deal with this problem is to take images and do a sorting of the stars. We build an empirical diagram where we take the stars, we divide them based on their colors (blue on the left, red on the right) and then we make a similar sorting in luminosity (bright stars are on top of the diagram and faint stars on the bottom of the diagram). The result is the CMD, where the position of each star is connected with the stelar structure and with its stellar stage, evolution. Today we will study how to read the CMD. We get information about the stellar system, about the universe in specific the formation time. 3  From the plot on the left we have stars in all evolutionary phases. RGB: stars burn helium. At the bottom right, outside of the plot we have the hydrogen burning limit: they are very faint stars close to the limit between standard stars and brown dwarfs. Since the stars in the CMD belong to a globular cluster, they can be considered in first approximation a SSP. So they have the same age, same chemical composition. The only difference between two different stars in the diagram is their initial mass. We know that stars evolve in different ways and time depending on their stellar mass. To investigate this we use theoretical tools. Stellar tracks The stellar evolutionary track is the curve on the CMD representing how the color and the luminosity of a star changes with time. In the theoretical plane we have luminosity against effective temperature (not magnitude against color from the observational point of view). Magnitude is observational counterpart of stellar luminosity. The mass shown in the figure on the right correspond to the initial mass. Each line in the diagram corresponds to the evolution of stars with different masses. Because of different masses they spend a different amount of time in different part of the lines. For example, stars spend a lot of time near the starting point, in the main sequence. They spend a shorter amount of time in evolved phases. Decreasing the mass the shape of the track changes and also the time of stars in different evolutionary phases changes as well depending on the stellar mass. Stars with low masses need more time to evolve. The track indicates how the luminosity/color of the stars changes with time. This is different from what we observe in the sky because in the sky we don’t have time to observe a star evolving. In the sky we observe a collection of stars in different evolutionary phases that have born at the same time. It is like observing a collection of snapshot of stars with different masses and the same age. Stellar Isochrones Going to the theoretical counterpart we have the isochrones. The stellar isochrone is the curve in the CMD that represents stars with the same age. On the left we have an example: CMD in theoretical plane with luminosity against temperature and this is the locus of stars that are characterized by a given chemical composition, unit distance from us and age of 1 Gyr old. Each point in the isochrone correspond to the point of the stellar track corresponding to the ge of 1 Gyr. What happens if we increase the age of the isochrone? Isochrones and age The shape of the isochrone, for fixed chemical composition and fixed distance, changes depending on the age of the stellar population. From CMD we can derive immediately the age of stellar population. The shape of the CMD changes with age in almost all evolutionary phases. But the point more sensitive to age variation is the turn off point, where the stars leave the main sequence (stars burn hydrogen in the core in the main sequence). The turn off is considered as the main chronometer provided by stellar evolution. The turn off is the point where the star leaves the main sequence. The brightness of the turn off depends on age. When the stellar population gets older the turn off point becomes fainter and colder. We have also some changes in other part of the CMD, for example the position of the sub giant branch, red giant branch are also sensitive to the age variation. The plot on the right is a theoretical one (luminosity vs temperature). We do not observe the total luminosity of a star, and the temperature. This are quantities that we can infer from observation, but they are not observed directly from the telescope. We need to mix theory with observations. Observations provide the magnitude in different filters, the digital number (counts on the CCD), whereas the theory provides evolutionary time, luminosity and effective temperature. We need to transfer the photon into theoretical quantities. From theory… to observations We need to transfer information from the theoretical to the observational plane and the other way around. Most information we gather from observations of stars come from the photons they emit. We have some relation that connect the observed properties of stars with the one predicted by stellar models. Spectroscopy and photometry have to be related to the properties predicted by stellar models. Bolometric magnitude: Mbol measures the total radiation of a star emitted across all wavelengths of the electromagnetic spectrum. The Mbol,Sun is a constant and the value is 4.74. LSun is used to normalize the luminosity with respect to the Sun. The bolometric magnitude is indicative to the total radiation of the star, the total radiation of the star over all the wavelengths of the electromagnetic spectrum. We cannot derive the bolometric magnitude with observations, because the telescopes we use are set to narrow windows of the spectrum. We cannot derive the integral of the area below the overall star spectrum. What we observe, 4 using filters, is the convolution of the light emitted by the stars. The transmission of the system composed of telescope plus filters. We observe flux in some intervals of the electromagnetic spectrum. We observe the magnitude in a given filter. So, we must connect the bolometric magnitude (integral of the spectrum) to the magnitude in a given filter. Absolute magnitude: MA in a given photometric band A, is related to the bolometric magnitude as: where BCA is the bolometric correction to the photometric band A. The bolometric correction depends on the specific filter we are using. From the theoretical point of view, we know the bolometric correction, and to transfer information from the theoretical to the observational plane we need MA and BCA. In the end we want the bolometric magnitude and to do that we need to calculate the bolometric correction. The absolute magnitude is the magnitude at a unit distance of 10 pc and stars are not located at unit distance. So what we observe is the apparent magnitude, to get the absolute one we need the information about the distance. The observed magnitude of a star, called apparent magnitude (mA), is related to the absolute magnitude as: where d is the distance (in parsec), AA the interstellar extinction in the photometric band A. The medium between us and the astronomical object is populated by gas and dust. The light that we observe is not the entire light emitted by the source. The extinction depends on the filter we are using. Going to UV we have a lot of absorption, while going to IR the amount of absorbed light is much smaller. The unit distance is when the distance modulus is 0 at a distance of 10 pc. What we discussed till now is correct for object close to us. We will investigate objects very far away in the universe and so we have to deal with high redshift objects. In high-redshift objects we must account for the fact that: 1) the redshifted spectrum is stretched through the bandwidth of the filter and so 2) the light that we observe through the filter comes from a bluer part of the spectral energy distribution because of the redshift. We need to use a correction that accounts for this phenomenon, it is the K correction. It depends on the filter, indicated in x in the formula below. The k-correction depends on the filter transmission, on the flux of the source and on the reddening. What is a star? The vast majority of stars we observe in the sky appears as point-like sources. They appear as point spread function (PSF) in the detector due to the diffraction image, instrumental tick. For close stars and big stars in term of angular diameter, it is possible to resolve the surface of the stars using interferometers. The ideal target to investigate stellar structures is the Sun. In first approximation they are black body. The structure of the Sun is illustrated in the figure on the left. The photosphere is the surface of the sun. If we look at images of the sun, what we observe is the photosphere. Going into the centre of the Sun we have convective zone, radiative zone and the core with a temperature of T = 15 000 000 K where we have the hydrogen burn. Why can we consider the Sun as a black body? The reason is that the light that we receive from a star has been released by the photosphere, where the optical depth – τ (the probability that a photon has an interaction with the stellar matter), is about 1. The light emitted by the star is characterized by the black body spectrum, whose energy distribution depends only on the effective temperature. So we have that blackbodies radiation is described by the Planck law where: - B is the spectral radiance [units: power per unit solid angle and per unit area normal to the propagations] - h is the Planck constant - k is the Boltzmann constant. 5 From the formula, the only variable is the temperature. Once we fix the temperature, we define the curve. There is a fast increase of intensity as function of the wavelength approaching a peak, and then there is a gentle decline with a lower slope. For hot curve the peak is around the blue wavelength. Decreasing the temperature, the peak is shifted towards the red. In the case of the Sun the peak of the Planck function is centred around the green. If we assume the star is a black body, the total flux is given by the following formula where is the Stefan-Boltzmann constant. The energy distribution depends only on the effective temperature. How can we infer the temperature of the star? We look at the color index. Color indices We take two filters and our telescope. In the example we take a blue and a red filter. We calculate the magnitude in the blue and red filter, we make the difference between these two magnitudes, and you see that the difference of the two magnitudes is indicative of the slope of the black body curve. In the case of a hot star the flux in the blue filter is more with respect to the flux in the red filter. A generic colour index (A-B) is defined as the difference of the magnitudes in two photometric filters. Color indices provide a measure of the slope of the black body curve. And therefore, of the temperature. Measuring the color has some advantages. For example, when we deal with magnitude we have to deal with distances. Luminosity of stars depends on distance and if we don’t know the distance we cannot study stellar population. But this is not true for the color. A given color is not dependent of stellar distance because it is the difference between two magnitudes, but it is affected by extinction: (𝐴 − 𝐵)0 = 𝑀𝐴 − 𝑀𝐵 = 𝑚𝐴 − 5 log(𝑑) + 5 − 𝐴𝐴 − 𝑚𝐵 + 5 log(𝑑) − 5 = (𝐴 − 𝐵) − (𝐴𝐴 − 𝐴𝐵 ) = (𝐴 − 𝐵) − 𝐸(𝐴 − 𝐵) We can compare colors of object at different distances. Luminosity is related to distance. We defined the color excess, or reddening, as. If stars are black bodies two magnitudes would be enough to constrain both stellar temperature and luminosity. Because once we know the effective temperature we know the bolometric flux of the star. This works in theory. But in reality, we don’t have a perfect black body function concerning stars, because you have absorption lines. Stars are blackbodies in first approximation. After being released by the photosphere where τ = 1, the photons cross the overlying stellar atmosphere, where τ < 1. It is the crossing of the atmosphere that introduces a dependence of the spectral energy distribution of the properties of the star, such as gravity and chemical composition of the star. So we don’t have only a dependence on the temperature, but also on gravity and chemical composition just looking at the spectrum of the star. When talking about chemical composition we include the abundance of the main elements, hydrogen and helium. Looking at the spectral line we can get information about the presence of the other chemical elements. We have to compare observations with theoretical models. They are models of stellar atmosphere to predict the spectral energy distribution of the emerging photons that approach the stellar atmosphere and they are mandatory to study the stellar spectrum and so to compute appropriate bolometric corrections to any given photometric filter of out telescope. From the figure on the left we have a comparison from theory and observation concerning the Sun. The black curve is the black body spectrum. The yellow curve is the observed one from space. Instead, if we observe from ground, we have the Earth atmosphere and so we have absorption features due to the Earth atmosphere and depending on the location of observation and so the spectrum we observe is the red one. Tu summary: in theory we have black body spectra, we derive the bolometric correction and we move from observed magnitude to properties of star. In reality the situation is much complex and we need to deal with theoretical models of stellar atmosphere. We need to understand the structure of the Earth atmosphere as well. Concerning the spectra, moving to low temperature stars, the spectrum becomes very complex because we start to be dominated by molecules in the star and in the earth atmosphere. The spectrum I s very different from a black body one. While for high temperature it is easy to identify the black body structure. While going to low temperature it is more difficult to define the continuum of the spectrum and the black body curve. Sometimes color is not a good indicator of the temperature for certain ranges of colors in a given color index because from Earth we have some region of the spectrum that cannot be observed due to absorption of Earth atmosphere. We try to use filters that are poorly affected by the Earth atmosphere. Those filters are J-H-K-L-M photometric bands. From theory to observations we can have that the CMD changes a little bit. CMD have different sensitivities to stellar parameters in different part of the CMD. The color is a proxy of stellar temperature but it cannot be a good indicator of temperature for certain ranges of colors. Changing color observing the same source we have different part of the CMD that represent in a good way the theorical CMD. 6 Absorption We want to find a link between the absolute magnitude, the bolometric luminosity of the star and the observed magnitude. We have a missing ingredient, which is the absorption. It indicates that there is some matter between us and the object. For this reason, we need to account for the amount of absorption. If we observe a star cluster, plot on the left, we can identify the members of the star cluster by using proper motion. But what we observe is that the sequences of stars in the cluster, left figure, are not as narrow as if we consider an isochrone, right figure. One of the reasons for the broadening is the fact that we have differential absorption. If we look in different direction of the sky, the amount of dust and gas between us and the star is different. This difference can be dramatic if we look at very different places in the galaxy. In the galactic plane the absorption is very strong, while looking at the poles of the galaxy the amount of dust is almost negligible. We can have the formation of the reddening from one point to another, even if the two points are close to each other. This process is called differential reddening, which is the variation of the reddening within a field of view. Stars in the same cluster are so absorbed in different way. This phenomenon is responsible for the broadening of the CMD. The broadening is physical but is not related to physics of the cluster, and we want to correct for this effect. Extinction Interstellar space is permeated by interstellar medium (ISM). ISM is composed of gas and dust. Dust is responsible for scattering the radiation. Interstellar gas tends to absorb and radiate radiation in different directions with respect to the direction of the incoming radiation that was then absorbed. The observed flux is related to the intrinsic one, in case of no absorption, by: where is the optical depth of the ISM at the observed wavelength. It depends on the wavelength. Extinction is not uniform along the stellar spectrum because varies as in the optical part of the spectrum. Therefore, the objects appear redder than they really are. Extinction is dramatic for short wavelength, but it is less serious in the NIR. The change in apparent magnitude at wavelength λ due to extinction is: 𝑚𝜆 − 𝑚𝜆,0 = −2.5 ∗ log(𝑒 −𝜏 ) = 2.5𝜏𝜆 log(𝑒) = 1.086 𝜏𝜆 The extinction at wavelength λ is:. Extinction law What is usually derived empirically is the so-called extinction law, for example the values of the ratio Aλ/AV at wavelength λ to that of the Johnson V band. The difference AB-AV is indicated as E(B-V) and the ratio AV/E(B-V) is denoted as RV. Accepted values of RV range from 3.1 to 3.3, although in peculiar directions it could be different. The values of RV can vary in different galactic and extragalactic environments. Gas and dust are responsible for extinction. Lecture 3 - THE FORMATION OF THE GALAXY: CONSTRAINTS FROM THE CMD We will discuss about application of the CMD. The reason why we study stars is to try to address issues of stellar astrophysics and today we will study the constraints of formation of galaxies by using the CMD. Lambda Cold Dark Matter model According to the standard model of universe formation the LCDM model is related to the Big Bang scenario. The Universe is characterized by cosmological constant (Lambda), associated to dark energy and cold dark matter. This model is considered as one of the most successful model in cosmology because it is able to predict several observations in the universe. Predictions from the Lambda-CDM model are in agreement with: 1. the existence and the structure of the cosmic microwaves background, so the picture of the distance universe in the microwave range. The fact that the universe is not uniform in the microwave range is a prediction of the Big Bang cosmology. 2. The accelerating expansion of the Universe. From the figure on the left, we have the distance modulus over the redshift/time. The constants are derived from observation of supernovae, standard candles. What you see is that the distribution of point is indicative of acceleration of the universe. It is a confirmation of the LCMD model. From the plot we tried also to disentangle the different values of the constants that are responsible for the present-day structure of the universe. We tried to understand if the points are consistent with the universe. Some of them will be dominated by matter and they will stop expanding at some point and eventually collapse again on the other side in the universe that is not dominated by matter and it will expand forever. The figure below explains the expansion of the universe and it is very important. It shows observational confirmation of the universe expansion and of the LCDM model. 7  3. The abundances of H, He, Li. According to this model, they are produced in the very early phases of the formation of the universe, during the Big Bang nucleosynthesis. The abundance is overall consistent with the Lambda-CDM. 4. Distribution of galaxies on large scale. Distribution of matter is in filamentary structure. The density decreases when we go outside the filaments. Lambda-CDM model agrees with the distribution of galaxies. One project that study the distribution of the galaxies in the universe is the 2dF Galaxy Redshift Survey. The missing-satellite problem Lambda-CDM is a quite good model, but it has some issues. Small issues can be an indication that the entire model is not working, or just that a small part of the scenario must be changed. Simulations based on the Lambda CDM model predict that dark matter clusters hierarchically. We expect ever increasing number of counts for smaller- and-smaller-sized dark matter halos. We can verify if those predictions are true by observing the galaxies, and in particular the satellite galaxies. The small size of dark matter should be the counter part of satellite galaxies of the Milky Way, the most famous one is the Magellanic clouds. In contrast to what is predicted by the Lambda-CDM model the number of dwarf galaxies is orders of magnitude lower than what expected from simulation. Is it an issue for the LCDM model or is there something missing in the model or observation? We try to constrain the galaxy formation using the CMD. We try to address the question: how did the Milky Way form? how did the universe form? Is the LCDM scenario correct? Are there issues? What is the contribution from dwarf galaxies to the building of the Milky Way and other galaxies? Galaxy formation To try to answer previous questions we use: theoretical models (theoretical isochrones), observations from Hubble Space Telescope, stellar isochrones, CMDs of 68 Globular Clusters (GC because they formed at high redshift, so it is easier to learn from the high redshift object. In particular when we want to understand the formation of galaxy). Muratov & Gnedin (2010) devised a semi-analytical theoretical model of the formation of a galaxy and its system of GC population. The model is built on top of cold dark matter galaxy-formation simulations. If the predictions from this model are correct, since it is derived from the Lambda-CDM model, everything is ok. The figure on the right shows an outcome of the theoretical simulations because on cold dark matter scenario. There is a plot of the age of families of globular clusters against metallicity. Each point is an average age of a sample of globular clusters with given bins of metallicity. Back to the last lecture: Bolometric Corrections The figure on the right represents an isochrone, which represents what we expect in the luminosity-temperature plane for SSP composed of stars with same age and same chemical composition. In the observational plane we plot magnitude against color, different from the theoretical plane. In real life we cannot measure luminosity and it is very challenging to measure the effective temperature for huge number of stars. It is convenient to move from theoretical plane to the observational one. The absolute magnitude (MA) in a given photometric band A, is defined in terms of bolometric magnitude (Mbol) as: 8 Where BCA is the bolometric correction to the photometric band A. We just need to convert the total luminosity in magnitude, apply the bolometric correction from theory, and for stellar evolution models we move from the theoretical to the observational plane. Back to the last lecture: Isochrones and age We are interested in reproducing the plot of Muratov & Gnedin from an observational point of view. We need to plot the age against the metallicity of the cluster. How can we derive the age? From the shape of the isochrones, which strongly depends on the age of the stellar population itself. We represent the same chemical composition but with different ages. The bottom part of the isochrone, which corresponds to small mass, has the isochrones overlapping, so we cannot clearly give an age to the stellar population. Whereas the brightness of the turn off strongly depends on age. The turn off is considered as a chronometer provided by stellar evolution to infer the age of simple stellar population. As the stellar population becomes older, the turning point becomes fainter and redder, because in an observational plot the magnitude increases in number and the color shift to the red. Back to the last lecture: Interstellar extinction Due to the presence of dust and gas in the interstellar medium between us and the object, we do not observe the absolute magnitude. The observed magnitude of a star, called apparent magnitude (m A), is related to the absolute magnitude as: where d is the distance (in parsec), AA the interstellar extinction that depends in the photometric band A. Metallicity There is another quantity we need to account: metallicity. The plot at the beginning relates age to metallicity. Stars are composed in first approximation by 3 quantities: X, Y and Z. X and Y are the mass fraction of hydrogen and helium, and Z is the mass fraction of metals, everything heavier than helium and hydrogen. It is challenging to measure the amount of quantity of metals, because there are plenty of them and it is not easy to identify them and measure their abundance. Usually, we take some elements as proxy of metallicity. The most used one is iron, which is the proxy of stellar metallicity. Iron abundance can be defined in different ways. Observationally, the traditional metal-abundance indicator is the quantity: The quantity on the right, after the minus, requires the sun symbol as below. If one assumes that the distribution of heavy elements that we see in the Sun is universal, the conversion from [Fe/H] to Z is given by: and the quantity log(Z/X)Sun is 1.61. So, using the empirical value of the solar Z/X ratio, we get: Once we know the metallicity, how can we study metallicity in an isochrone? Isochrones with same age but different metallicity are shown in the figure on the right. According to the definition of Fe/H, if the star has the same metallicity of the Sun, we have that Fe/H is equal to 0. The blue isochrone (Fe/H = -2.0) corresponds to a very metal poor stellar population. Solar metallicity abundance means Fe/H equal to 0. Over/under solar abundance means >0/ −7 (M~10,000 solar masses). The internal kinematics reveal that UFD have mass to light ratio M/L > 100, hence they are dark matter dominated. An approach to constraint the amount of dark matter of the UFD is by using stellar evolution. When dealing with a new class of objects, what is the difference between UFD and the other objects populating the halo? Maybe for UFD the classification can be easier because for GC we do not have a significance presence of dark matter. Globular Clusters are consistent with having no dark matter, in fact their mass to light ratio is M/L~2. Galaxies have significant dark matter: classical dwarfs have mass to light ratio M/L~10 and ultra-faint dwarfs have mass to light ratio M/L>100. A powerful plot used to classify Gs, GC and UFD is shown in the figure on the left. We pot the luminosity relatively to the Sun luminosity against the diameter of the object. The three classes populate different regions of the plot but there is not a sharp separation between classical and UFD. Is there any significant different formation between classical dwarf and UFD or the difference is related to something that occurred during evolution? Ultra-faint dwarfs look like extension of dwarf galaxies. The Big question: Going back to the classification of fossils. Now that we discovered UFD Gs which are great candidates of the true fossils, do true- fossil galaxies exist? Are the ultra-faint dwarfs true-fossil galaxies? HST infers the age of six ultra-faint dwarf To investigate the big question, we used the HST. We got the CMD of 6 UFD galaxies, as shown on the right. We have to understand if they are true fossils so if they are old stellar population or young stellar population. By definition true fossils are galaxies that formed their stars before reionization and after reionization star formation finished, so reionization stopped the star formation. The first approach is taking isochrones and deriving the age by fitting isochrones. The other approach is taking a fiducial line of an already known globular cluster, that is a very old stellar system formed during the period of the reionization, and 13 comparing the position of the fiducial line with the CMD of the object. This is what have been done with the figure shown on top. The green line and points are stars belonging to a GC that formed before reionization, more than 13 Gyrs ago. It is a very metal poor GC. In fact, for true fossils stars are very metal poor stars because they formed before reionization. They are made by the pristine material that was already polluted by population III stars ejecta but it is still a very metal poor material. Comparison between M92 GC and CMD of UFD are consistent with each other. The conclusion was that at least 80 % of stars in the UFD galaxies formed at redshift of z=6 or more and 100% of stars formed at z=3. So the star formation in the dark matter in sub-halos that surround UFD was suppressed by something that occurred at redshift around 6 (e.g. the reionization). This is a strong indication that UFD are true satellites. It is a confirmation of the theory where we suggested that some dark matter halos are not able to form stars, while there are some dark atter halos that are surviving and forming stars. UFD: dark matter halos where star formation was shuttled down by reionization. Binaries We talked about SSP composed by single stars that are distributed on the CMD. In SSP all stars are made by the same material, have the same age, same chemical composition, same distance. But there are also binary systems. If the stellar system is close to us we are able to distinguish the two components and if they interact with each other they will appear as single stars. We can plot the two separate stars along the CMD, differentiating the brighter star with the other. But if star systems are far from us we cannot resolve the two stars. Unresolved binaries If we look to stars clusters far away from us, we cannot distinguish the binaries. In specific in a cluster, binaries form very very close to each other, otherwise if they have a low binding energy, because they are distance one from the other, they would be break apart because of stellar interaction. How can we deal with the binary system in the CMD? We infer the properties of binaries. The luminosity and the mass of stars are connected with each other. In the CMD, a point corresponds both to luminosity and to a given mass. When fitting the stellar population with isochrones, for each star we can read in the corresponding point of the isochrone its parameters, so luminosity and mass. So binary system will appear as a single point-like source and the light of the two sources will combine together. NOT the magnitude of the two star is the sum of the two stars! But the flux of the binary system is given by the sum of the two fluxes. Let’s consider the two components of an unresolved binary system and indicate with m 1, m2, F1, and F2 their magnitudes and fluxes. The light of the two stars combines together. The binary system will appear as a single point-like source with magnitude: Indeed: m1 = -2.5 log(F1) m2 = -2.5 log(F2) mbin = -2.5 log(F1 + F2) = -2.5 log[ F1 (1 + F2 / F1) ] = -2.5 log(F1) - 2.5 log( 1 + F2 / F1 ) = m1 - 2.5 log(1+F2/F1) With this formula we immediately have the information to calculate the position of the binary system in the CMD. Once we have the fluxes of the two stars/ masses of the two stars we have the info to calculate the position of the star in the CMD. Let’s consider some cases. 1. the two stars have the same flux and so the same mass. So we have that F 1/F2 = 1 mbin= m1 - 2.5 log ( 1+ F2 / F1) = m1 - 2.5 log ( 1 + 1 ) = m1 - 2.5 log( 2 ) = m1 - 0.752 The binary system, as a single point, will appear 0.752 mag brighter than each single star parallel to the main sequence. There is a shift of the sequence parallel to the main sequence in the CMD. As an example, the V and I magnitudes of two equal-mass binaries are: Vbin = V1 - 0.752, Ibin = I1 - 0.752. Their color is Vbin - Ibin= (V1 - 0.752) - (I1 - 0.752) = V1 - I1. The binary system composed of equal-mass stars has the same color as each single star. 2. In the case of a simple stellar population the fluxes are related to the stellar masses: M1, M2. As a consequence, the luminosity of the binary system will depend on the mass ratio q = M2/M1. In this case we assume: M1 ≥ M2, so 0 ≤ q ≤ 1. Equal-mass binaries are binary systems formed by two stars with the same mass M1=M2 so for q = 1 that we discussed above. For different values of q we have the binary system that describes a curve shown in the plot on the right. How do we move from mass (q value) to luminosity? We use the mass luminosity relations that are provided by the isochrones. We know the mass and the luminosity of the primary star, we know the mass ratio. From the mass ratio we derive the mass of the secondary star (M2 = qM1) and then we go to the isochrones and by using the mass luminosity relation used to make the isochrone we get the 14 luminosity and magnitude of secondary star. Once we get luminosity and magnitude, so the flux we can put the flux of the secondary star in the relation defined above and we build the curve. When the stars evolve, the binary system evolve from the main sequence to the white dwarf cooling sequence. There are binary systems also in the WD cooling sequence. We discussed about binaries for which both components belong to the main sequence. The simple case is that each component of the binary system evolves in an independent way. They are linked from the gravitational point of view, but not in the stellar evolution, they do not exchange mass. But often binary systems exchange mass and are responsible for strange phenomena. Till now we discussed about stars that produce energy by burning something. In the case of the main sequence, they burn hydrogen, in the case of the horizontal branch they burn helium. So, we have that nuclear reactions are responsible for the production of energy. What happens when the fuel for nuclear rection is finished? White dwarfs They are the evolutionary end stage of more than 95% of all stars. WD are dying stars. They are stellar core remnants composed mostly of electron degenerate matter. The plot on the right shows the CMD of Sun stars. They are the final evolutionary state of stars with masses smaller than 8-10 MSun. With masses > 8/10 MSun they explode in supernova. The core temperature of 8-10 MSun stars fuses C but no Ne. Hence, a O-Mg-Ne white dwarf may form. Stars of very low mass will not be able to fuse helium, hence, a He white dwarf may form. Ages from the white dwarfs cooling sequence The evolution of a white dwarf is a cooling process with a strong age-luminosity relation. WD phase is just described by a process of cooling. The energy emitted by the star is just related to the cooling process of the star. The figure on the left shows the simulation of the WD cooling sequence. We can observe that increasing the age, the distribution of stars in the WD cooling sequence changes. In particular, we see that the extension of the sequence increases when the stellar population gets older. We can make this comparison using the luminosity function, which refers to the counting of stars in a given interval of luminosity. The simulation on the right shows the luminosity function, we put the number of stars against the luminosity of the stars. Increasing the age, the luminosity function of stars/magnitude changes. In red we have LF that stopped in the first case, at 2 Gyrs, in the second case at 3 Gyrs. We see that the position of the peak changes significantly. In blue is the same plot with stellar population of 13 Gyrs. The sensitivity of the method changes, and decrease going to old stellar population. In red we see that for a different in age of 1 Gyr old the difference in luminosity is of 0.5 mag. Going at older ages, the magnitude difference is 0.2 mag for a different in age of 1 Gyr. Given age difference correspond to a small luminosity difference. For old stellar population position of the peak shifted to fainter magnitude. So we need to get very precise luminosity determination of very faint stars. This is a complex determination because we need to derive precisely magnitudes of faint WD, which means that the luminosities of stars we are talking about are 28-27 mag. And these magnitudes correspond to the GC that appear closest to us. Comparing observed and simulated WD cooling sequence, you can infer the age of the stelar population. White dwarfs cooling sequence Why do we care about the age determination of the WD cooling sequence? We saw that we can derive precise age determination from stellar systems using the turn off point. The vertical method was based on the relative luminosity of the turn off point and the horizontal branch level of stars. We used stars brighter than the faint WD. Why age of WD cooling sequence? Because the ages derived from the turn off, or horizontal branch position, are based on certain physics. We are dealing with stars that burn material to produce their luminosity. It is very important to get ages determination using positions that are independent with each other. For WD, the cooling process follow a different physics with respect to the ones that we have for stars producing energy by nuclear reaction. So deriving the age of WD means derive independent age from what we can get using main sequence stars. The position of the Main Sequence and the turn off in the CMD depends on metallicity of the stellar population. As the stellar population gets older, the turning point becomes fainter and redder. The entire CMD shifts towards the red. Age-metallicity relation and galaxy formation From the sequences we can age reliable age determination and we can get important constraints on the structure and the evolution of the galaxies. What about the possibility that the age we derived from the turn off is not correct? It is due to uncertainties in our modelling of hydrogen burning in stars. So all the consequences that we made for the LCDM model for the universe are not correct. This is the reason we want to investigate the WD cooling sequence in GC. The challenge is that in GC that appear closest to us, the WD cooling sequence approaches very faint magnitudes. So it takes very long time for the telescope to do observation. The age determination of the WD cooling sequence has also some advantages. 15 So we studied how we can get the age of stars using different techniques and different position along the CMD described by different physics. Lecture 5 - THE FORMATION OF THE GALAXY: CONSTRAINTS FROM THE CMD We continue with the impact of the CMD with the investigation of the formation and the evolution of the galaxies. We discussed about binary stars. We talked about unresolved binaries. Stars in the binary system are very closed to each other as seen very far away in the sky, so you cannot distinguish them. The binary system is seen as a single star and the light from the two stars combines together. The magnitude of the binary is provided by the sum of the two fluxes of the two stars. If we look at binaries in a star cluster, it is easy to derive the light of the two components, because their light is related to the masses. If we know the mass of the two stars, the binary system luminosity depends on the two masses and the mass ratio. The mass ratio is called q (between 0 and 1) and it is defined as that m2, the secondary star, is the smallest star. Fixing the mass of a primary star, by varying the mass ratio the binary system will describe a line in the diagram parallel to the fiducial line. As far as you change the mass of the second, the line will change and increasing the mass of the secondary star/the mass ratio the binary system become brighter and redder. Binary system of two stars of equal mass, the mass ratio = 1, the binary system will have the same color as the single star, but the luminosity will be brighter of a factor of 0.725 mag than the single star. Once we disentangle the properties of the two stars of the binary system we can derive the properties of the binary system in the SSP. The alternative approach to investigate binaries is spectroscopy. You need to observe/analyse stars one at a time. So it takes a large amount of observational time. Instead, using the technique of the mass and the flux you just need two images in two different filters and you can analyse a large number of binaries. And we apply this technique to constrain the dark matter content of single UFD. The binary system we are considering at the moment deals with stars that evolve independently from the other star in the binary. The two stars are not interacting with each other. They evolve independently. What discussed about Binary system can be related to triple or multiple systems. Our instrumentation Every time looking at observation you need to look for the instrumentation used because you can under/over estimate the results. Hubble Space Telescopes: mirror diameter of 2.4 meters (it is a small telescope, old technology), wavelength range from ~0.1 (UV) to 1.7 (IR) μm (WFC3). It was launched in 1990. It orbits in low Earth orbit in the lagrangian point at an altitude of ~540 km and a period of ~55 min. It had five Shuttle servicing missions. The cost > 10 billion $. The most-used instruments on HST are: - the Wide Field Planetary Camera 2 (1993-2009). It includes four cameras composed of 800x800 pixels each. – WF2, WF3, WF4 Plate scale 0.10x0.10 arcsec/pixel – Planetary Camera Plate scale 0.05x0.05 arcsec/pixel Wavelength range: ~1200–10000 - The Advanced Camera for Surveys (ACS) 2009 – present It includes three channels: 1) High Resolution Channel (HRC) Field of view of 29x26 square arcsec, Wavelength range 1700 – 11000 Å, Plate-scale: 0.027 arcsec/pixel. It is not active anymore. Images of planets. 2) Solar Blind Channel (SBC) Field of view: of 34.6x30.5 arcsec, Wavelength range: 1150 – 1700 Å, Plate-scale: 0.032 arcsec/pixel. 3) Wide Field Channel (WFC) of ACS field of view: 202x202 square arcsec, Plate-scale: 0.05 arcsec/pixel. Wavelength range: 3500-11000 Å (visible, some in IR). It is a camera on board of HST now. It has also some narrow filters to observe, for example, the H alpha. It is the one we are going to use. Change Transfer Efficience loss There are technical staff you need to know when talking about observations. The following is responsible for some mistakes in the observational catalogue. The fraction of electrons that are successfully moved from one pixel to another during read-out is described by the charge transfer efficiency (CTE). Normal charge transfer efficiencies are 0.99999 – 0.999999, (one photoelectron is lost for every 100000 to 1000000 shifts!) If the CTE is only 0.999, you couldn't read most of the CCD. CCDs that have a very low CTE will leave streaks which are caused by charge/electrons being left behind after a transfer. Point-Spread Function Photometry Each star appears as a point like shape structure. All the point-like sources imaged by the telescope system can be represented by a point-spread function (PSF). The PSF gives ‘the shape’ of a star on the detector. Its amplitude will scale linearly with the brightness of the star forming the image. The shape depends on the distortion of the detector, position of stars with respect to the detector, the system composed by the telescope and the star itself. In principle the recipe to derive the PSF model is simple: we must identify stars in our image, determine the sky under the stars, use isolate stars to derive the PSF model. To measure stellar fluxes and positions we must fit the PSF model to all the star observed in the image (allowing for the fact that the stellar image sits on top of the sky). 16 White dwarf They are the evolutionary end stage of more than 95% of all stars. They are stellar core remnants composed mostly of matter in electron degenerate state. They are the final evolutionary state of stars with masses smaller than 8-10 MSun. The core temperature of 8-10 MSun stars fuses C but no Ne. Hence, a O-Mg-Ne white dwarf may form. Stars of very low mass will not be able to fuse helium, hence, a He white dwarf may form. All stars of 8 -10 MSun and less, depending on their metallicity, will finish their life as WD. They are a powerful tool to constrain the age of stellar population. We use age of star clusters to infer important properties of the galaxies and the model that describes the universe (for example the study of the age of 68 GC to constrain the Lambda-CDM scenario for the big bang). We may have that the physics of hydrogen burning in the core is not correct. So to have a correct estimate of the age we need to use other technique. We need to confirm the age of the stellar population studying different portion of the CMD. This is why we study the age determination of the WD cooling sequence. The physics that describes the WD is different from the one describing stars that burn hydrogen. The evolution of WD is described by the cooling, characterized by a strong relation between the age of the stellar population and the luminosity, as shown in the figure on the left. The distribution of stars in WD cooling sequence changes depending on the age, in particular the bulk of stars becomes fainter and redder when the stellar population becomes older. We can derive a quantitative determination of this phenomenon by using the luminosity function. LF are count of star per interval of magnitudes. The figure on the right shows a simulation of the luminosity functions of WD cooling sequence for SSP with different ages. In red we compare the LF of the WDCS for stellar population of 2-3 Gyrs. We see that the distribution of stars is different and in particular the position of the peak of the LF is different. Peak position changes and become fainter with the luminosity. And the separation in magnitude for a fixed age difference become smaller when the stars become older. This is a powerful tool to derive the age. It is challenging when dealing with old stellar population because the peak separation gets smaller, and the luminosity of the stars becomes fainter. You need precise observations for very faint stars. They did a study on the GC NGC6397, which is the cluster that appears closest one to us. White Dwarfs cooling sequence The main challenge is that WD are faint stars. An example is the 47 Tuc where you reach a magnitude of 30 mag. What is the reason in deriving the age from this technique if it is very expensive and if it can be done only for few clusters? The first advantage is the dependence on metallicity. When we investigate ages by using the turn off, the position of the MS turn off in the CMD depends on the metallicity, not dependent only on age. Depending on the metallicity, the position of the turn off becomes redder and fainter depending on the metallicity. In the case of the white dwarf what happens? Let’s deal with the big question, how a galaxy form? The figure shows in red the points that are clusters located in the outer halo of the galaxy. Blue points are clusters close to the centre of the galaxy. The two colors are characterized by a different age metallicity relation. In the case of blue points there is an increase in metallicity in a short amount of time. In 0.5/1 Gyr we have a change from very metal poor metallicity regime (-2.5) to metallicity of -0.5. In red we have a prolonged GC formation. The age metallicity relation is consistent with the prediction of the Lambda-CDM scenario. This GC formed in dwarf galaxies accreted by the Milky Way according to the LCDM scenario. The impact of the plot in our understanding of the galaxy is huge and it is fundamental whether those relations are real an not due to some uncertainties in the age determination derived from the MS turn off. Age-metallicity relation and galaxy formation Derive the age from the WD cooling sequence is expensive in terms of telescope time and money and it is not possible to do it for clusters far away from us. The end of the WDCS can be observed in a few nearby GCs alone. How do we deal with this problem? Is the age-metallicity relation for the two GC in the plot above real or an artefact. How can we solve this problem? We need to understand if there is a major issue in the determination of the ages. We can derive ages only for few clusters. If we want to understand if the ages are reliable, we have to go into two different regions of the age metallicity relation: in the metal rich regime and in the metal poor regime. So to tell how the clusters are behaving one with respect to the other we take the two diagrams and we put them one on top of the other in an absolute magnitude scale. In the figure on the right the red plot refers to a metal poor cluster (NGC6397 which has the shortest distance modulus), whereas the black plot refers to the metal rich cluster (47 Tuc, one of the closest cluster to us). We are exploring two clusters in the different region of the age metallicity plane. The CMD of the metal poor cluster, considering the main sequence, is brighter and bluer with respect to the metal rich cluster. This is what we expect from theory. For fixed age, the turn off becomes redder and fainter. What about the WD? In contrast to what we saw for the main sequence, the WDs overlap of the two metal rich and poor cluster is perfect, as shown in the figure as well. We cannot clearly distinguish between a metal rich or a metal poor WD. This is an empirical demonstration that, in contrast to the main sequence, in the position of the WDCS in the CMD the stars do not depend on the metallicity. In fact, the process responsible for the luminosity of the star is the 17 cooling process. What we can do is comparing the age derived from the white dwarf cooling sequence with the age derived by main sequence turn off. Ages inferred from the WDCSs and on the MS turn off are based on different physics. WDCSs are crucial to validate MS turn off ages. The comparison between the WDCs reveals that 47 Tuc is ~1/2 Gyr younger than inferred for the metal-poor cluster NGC 6397. Metal-rich clusters (like 47 Tucanae) formed later than metal-poor halo clusters (like NGC 6397). We confirmed from independent methods that metal rich and metal poor stars formed in different epochs and there are no significant errors in the determination of the age. We can trust age from old techniques. The WD age determination confirms the main sequence age determination. Metal rich and metal poor cluster formed at different epoch, and we can trust ages derived from old techniques. The strange case of NGC6791… NGC6791 is a ~8 Gyr old Galactic simple population open cluster in the disk of the Milky Way. It does not exhibit evidence of multiple stellar populations, as observed in 2008. It is a good approximation of a single isochrone. From the age determination using the main sequence turn off in 2008, it was revealed that the age of the cluster was 8 Gyrs old. It is one of the oldest open clusters of the MW. It is quite close to us and so it is a good test case to derive ages from WD. The first attempt to derive the age of the stellar population was in 2005. The first deep luminosity function of the WDCS indicates that NGC6791 is ~2.5 Gyr old, in sharp contrast with results obtained from the main sequence turn off. Possible consequences: one consequence is that either the age inferred from MS turn-off or from WDCSs (or both) are wrong. The other consequence is that there are exotic population of Pure-Helium White Dwarfs. There is a surprising fact: the White Dwarfs Cooling Sequence of NGC6791 exhibits two distinct peaks. Deeper HST reveals a second (unexpected) peak in the WDCS luminosity function. The upper peak is consistent with the young stellar population of 4 Gyr, and the lowest peak is consistent with stellar population of 8 Gyr. Two populations of pure-He WDs and classic WDs? The solution is that there are unresolved binaries. To test this possibility is that we can measure the fraction of binaries in the main sequence (around 32%). We should expect the same fraction. We can do also a simulation of stars in WDCS, we have the double peak using the same fraction of binaries of the main sequence. Method to estimate the fraction of binaries of a stellar population. We move on the main sequence and we search for binary systems composed of two main sequence binaries. We know that in a SSP the position of the binary system in the CMD depends on the mass of the two components. Moreover, binaries are distributed on the right side of the main sequence. The position depends on the mass ratio and if we fix the mass of the primary star and we increase the mass ratio the binary system will appear redder and brighter than the primary star, following the blue curve and it will approach the star symbol where the two components of the binary system have the same mass. In this case the binary system will appear as a point-like source with exactly the same color as each single component but 0.752 magnitudes brighter. So we can immediately infer the fraction of binaries of SSP, because they are redder and brighter than the main sequence. It allows to infer the binarity for almost all the binary systems in a star cluster including faint binaries. But in reality it is not completely true because due to observational errors, the position of stars in the CMD is a bit spread in color and in magnitude. Moreover, stars are not distributed on an isochrone but there is some broadening due to observational errors. If binary has small mass ratio, the position of the binary system is very close to the fiducial line and it is very difficult to disentangle between true binary system with small mass ratio and single stars that have large observational errors. So, in real life we are able to infer the presence of binaries only with a large mass ratio, bigger than 0.5/0.6. We cannot detect binaries for stars that are too faint because of observational errors and we cannot disentangle between binaries and single stars for stars close to the main sequence turn off because line of equal mass ratio binaries cross with each other and merge with the fiducial line of single stars. From the figure on the right you see that there is a specific region in the CMD for which you find almost binaries, and the region has a value of q>0.5. So you need to count the stars of region A, count the stars of region B and take the ratio. But remember that you have contamination of field stars and contamination of apparent binaries. They appear to us as a binary system along our line of sight, but they are physical unrelated. So when we make the ratio between region A and B we are taking into account also the apparent binaries. We need to account for them and we use the artificial star method: we generate fake stars in the field of view using the PSF model, we add them in the image, we reduce them by using the same technique that we used for real stars and we infer the CMD. We know that all fake stars are single stars, stars in region B are indicative of the fraction of apparent binaries. Concerning field stars contamination: we use the proper motion if it is relevant. Otherwise we need to account for field stars contamination by looking at a filed that is outside the field of the galaxy, but not too far so that the distribution of filed stars can be approximated to the distribution of stars in front of the cluster. We estimated the contamination of field stars in the two regions (A and B). 18 Lecture 6 - STELLAR SPECTROSCOPY Spectroscopy is used to infer the chemical composition of stars. Photometry: we investigate the integrated light, over all wavelength or at least over a given range of wavelengths. Spectroscopy: we study the rainbow. In specific we spread the light in term of wavelengths, and we analyse the flux as a function of the wavelength. Form spectra we can get chemical composition, effective temperature, gravity of stars. Photometry and spectroscopy are studied together because they are complementary. The main advantage of spectroscopy with respect to photometry is that we have a detailed analysis of the spectrum, so we don’t investigate light in big region of the spectrum but we investigate the features itself of the spectrum so we can infer detailed abundances of each element. We investigate the distinct spectral lines, molecular bands in the stellar spectrum. But on the other side since to do spectroscopy we need to spread out the light we have limitations in terms of stellar luminosity because when we spread out the light we reduce the signal to noise for each pixel of the CCD, so we are limited to bright stars. While with photometry we approach very faint magnitudes. Spectroscopy is the study of stellar atmosphere, because most of the information of stellar spectra come from the stellar atmosphere. Stellar atmospheres are the most important sources of radiation in the universe. They are wonderful physics laboratories, are unique windows on stellar interiors and stellar spectra contain a fossil record of the history of the cosmos. Concerning the origin of the elements: How, when and where were the elements produced? Stellar absorption line formation You have an hot source + a prism: the light is spread out and you see a continuum spectrum. A cool, thin gas seen in front of a hot source produces absorption lines. The lines refer to the chemical composition of the stellar atmosphere. In the continuum region, τ (optical depth: probability of a photon to interact with matter) is low and we see primarily the background. At the wavelengths of spectral lines, τ is large and we see the intensity characteristic of the temperature of the cool gas. Since the temperature of the stellar atmosphere is lower than central temperature of the star, the lines appear as absorption features. We can have some emission lines but those are phenomena produced in disk around the star, phenomena external to the star. Most of the lines are absorption lines. To quantify the level of the continuum spectrum and the depth of the absorption line we plot the intensity as a function of the wavelength. In the real spectrum of the stars there are a lot of lines telling info about the structure of the star and the interstellar medium between us and the source. Stars and radiation The photosphere is the stellar surface. In the photosphere the transfer of energy occurs through radiation. In the chromosphere, corona and solar wind the free streaming is connected with the radiation. Today we will study information coming from the stellar photosphere. When we observe the stellar spectrum we can detect some lines coming from the chromosphere. The Planck function is defined by the temperature of the body and the behaviour of the curve depends on the temperature. Increasing the temperature, the position of the peak of the Planck function is shifted to the blue. Hot stars are blue and cold stars are red. There are some approximations concerning the plank function, the Wien in the UV and the Rayleigh-Jeans in the IR regime. In the spectrum of a star, we see a continuum, which is related to the black body. Extracting information from the spectrum We extract information both on chemical composition and on the properties of the black body. The first information that we get is the spectral type and photometric classification of the stars. From spectra we can infer precise values of Effective temperature, Surface gravity, metallicity and chemical composition. Abundance Scales When we describe a star, we talk about the abundance of three components (hydrogen, helium and metals=all elements that are not H and He). We talk about abundance using the mass fraction (X, Y and Z). Most of the sun is composed by hydrogen X = 0.74. For helium we have Y = 0.25, for metals is Z = 0.01. Metals are a tiny fraction with respect H and He: the 42% of metals is oxygen, then we have carbon, neon, magnesium, nitrogen, iron, silicon. We use different scale to indicate the same quantities. We have the 12 scale: 19 where nX is the number of elements and nH is the number of hydrogen. Another scale is the [] scale: where X is an element. An abundance equal to zero means that the star has an abundance which is equal to the one of the Sun. it is the iron abundance of the most metal rich known stars in the galaxy. There are different technique to infer the chemical abundance: the logarithmic one (which is the 12 scale). For the sun we have the elemental abundance of the photosphere. This elemental abundance that we infer from spectra of the solar photosphere can be compared with the chemical composition of the meteorites, which formed from the pristine cloud of the solar nebula. So the chemical composition of meteorites is indicative of the chemical composition of the Sun. Line broadening Each spectrum is characterized by the spectral resolution which is indicative of the distance in terms of wavelength between two lines. High resolution means able to distinguish lines that are close to each other. Three main components: 1) Natural width: the line is not a delta Dirac but it is a broaden line. The profile is Lorentzian and very narrow due to the Heisenberg uncertainty principle → ΔEΔt = h/2π. The transition between two identical levels in different atoms can produce photons with a certain energy but with slightly different energies. As a consequence, the spectral lines are not infinitely sharp (they are not delta Dirac) in wavelength (or frequency) but exhibit a spread in wavelength that is described by the Lorentz function. 2) Pressure width (Lorentzian profile) due to collisions between particles. It mostly affects the shape of the wings of the spectral lines. 3) Thermal (Doppler) width (Gaussian profile, very narrow). Maxwell-Boltzmann distribution. Thermal motions of the atoms randomly distribute the shift. More broadening splits and shifts - Zeeman. Atoms in strong magnetic fields can align in quantum ways causing slight separations in the energies of atoms in the same excitation levels. This phenomenon splits the lines into multiple components. The splitting depends on the magnetic-field strength. - Stark: Perturbation by electric fields. We need to disentangle between these effects. The observed profile is a combination of the broadening discussed before. The advantage is that in the line profile we have information related to all these phenomena. Line broadening: stellar rotation We have two stars. One is rotating and the other is not. The not rotating star has a narrow line and the broaden is associated with the broadening effects discussed before. If the star is rotating the broadening of the line is associated with the rotation of the star. Different parts of the star are characterized by the different rotational velocity and so different doppler effect in different part of the star. Some stars rotate so fast that they are close to break apart. Hydrogen and helium lines Lyman series (from n=1): visible in the UV. Balmer transition (from n=2): visible in the Optical. Paschen transition (from n=3): visible in the NIR. Helium is the second most-abundant element in stars. 25% of the sun, in term of mass, is composed of helium. Helium lines are detectable in very hot stars (O-B). It is difficult to detect He in cold stars. If we observe an old stellar population (UFD, GC), where all stars formed at high redshift so hot and massive stars disappear, it is challenging to infer helium abundance in these stars. The depth of the helium line is 10 % with respect to the continuum in the best cases. In the majority of stars detected in the sky is difficult to detect helium line and it is detectable “easily” in hot stars. Metal lines Metal lines become stronger when effective temperature decreases. Dominate the spectra of F, G, K stars. Chemical compositions are derived from spectroscopy. If we consider photometry → photometry and stellar magnitudes are the convolution of the stellar spectra with the transmission of the filter. The stellar magnitudes are the convolution/ integral of the filter transmission plus the spectrum plus the response of the telescope. Johnson system is UBVRI. Observing the same stars in different filters we can get information also on the chemical composition of 20 the star. By using photometry we can infer the chemical composition of stars. With photometry we approach very faint stars and a lot of them. Molecular lines Decreasing again the temperature we have molecules. Molecular lines form in cool stars (M-, L-, T-types). The stellar flux is significantly reduced in the region of the spectrum where we have the molecular transission. We have different transition. Electron transitions are visible and UV lines. Vibrational transitions are Infrared lines. Rotational transitions are Radio-wave lines. Stars are divided in different spectral type depending on the shape of the spectrum and on the temperature (OBAFGKM). Depending on the spectral type and on the temperature of the stars, we have specific features present in the spectrum. Hot stars: helium. Stars with 20 000 – 7 000 K: hydrogen. Cold stars: metal such iron, calcium. Stars with 3000 K: molecules (titan oxygen molecule, water molecule). Application: Ages from the MS knee Method to derive the age based on the near infrared photometry, so we observe the CMD in the infrared. The plot on the right shows an isochrone in the near infrared. The Main-Sequence knee is a feature of the CMD caused by the collision induced absorption of molecular hydrogen and other molecules. It is well visible in CMDs made with near-infrared photometry. The color in a certain interval of luminosity is proportional to the temperature and decreases with the temperature. At some point we have the main sequence knee where when the color is not representative on the color anymore. But we have a dramatic change in the direction of the main sequence. We use this property of the CMD to infer the age. If we take stellar population with different ages the vertical distance between the knee and the turn off is indicative of the age of the stellar population. Increasing the age of the stellar population the position of the main sequence knee is fixed. What changes is the position of the main sequence turn off. The turn off becomes bluer and brighter as the stellar population gets younger. As the stellar population gets older, the vertical distance decreases. The magnitude difference between the Main-Sequence turn-off and the Main-Sequence knee is used to infer the age of star clusters. Advantages: - Not dependent on cluster distance - Not dependent on cluster extinction - Not dependent on photometric calibration. This is because the age determination is based on the relative vertical distance between two points in the CMD. So if I make some mistakes in the calibration, determining the photometric zero point, does not matter because I would do the same error for bright turn off stars and for faint main sequence knee stars. The magnitudes between the two points are not affected by such error. - large number of stars because the number of small stars in the main sequence knee is high compared with the number of stars in an evolved phase like the horizontal branch. You don’t have to deal with variable stars. Disadvantages - MS-knee stars have often faint luminosities - If we go at low temperature we have the effects of molecules, including oxygen. - The luminosity of the MS knee is strongly affected by oxygen abundance. - From plot on the right. Stellar populations with the same age but different oxygen abundances exhibit MS knees with different luminosities. Concerning the MS turn off and MS are narrow and similar to the isochrones. Instead for the MS knee we have a broadening of the sequence and each of the sequence corresponds to a different population with different content of oxygen. Each of the population is characterized by different knee position and it is not easy to disentangle the knee of the distinct stellar population. In case of multiple stellar population system we have the sensitivity of the position of the main sequence knee to the chemical composition. In particular water in stars affect the luminosity in the near infrared and they are responsible for multiple sequences shown in the plot. Lecture 7 - STELLAR SPECTROSCOPY Today we discuss about extra solar planets, the cosmologic lithium problem (apparent discrepancy between lithium abundance observed and the one predicted by the Big Bang nucleosynthesis), spectroscopic determination of the properties of stars. Concerning the age determination with infrared photometry, the position of the main sequence knee does not change, what changes is the position of the main sequence turn off. This is because stars at the main sequence knee are not evolved, they are low mass stars. 21 Most-relevant stellar parameters How from stellar spectra we infer stellar parameter: effective temperature, gravity, chemical abundance of stars. There are different approaches. Today we will focus on the spectroscopic approach. We will see later how to derive the same parameters with photometric techniques. The effective temperature is the temperature of the black body which is characterized by the same luminosity and radius of the real star. Metals: no H nor He. Z = 0.018 is the Sun case The number of elements heavier than He is high so difficult to estimate Z. Usually it cannot be possible to derive the chemical abundance of metals, so we derive the chemical abundance of iron. Iron abundance in first approximation can be used as proxy of stellar metallicity. So we derive Fe/H. Fe/H = 0 corresponds to a solar metallicity star, so a mass fraction Z = 0.018. Concerning the structure of stellar spectrum. In first approximation the stellar spectrum can be considered as made of two main components: the continuum, approximated as a black body curve, and on top of it, regardless the approximation of the continuum of the black body curve which is good or not, we have the absorption lines. The spectrum is expressed in flux as a function of the wavelength. But for practical purposes when we want to derive the stellar parameters and elemental abundances from stellar spectra, it is convenient not to use the spectrum itself, but the normalized one. So we take the observed spectrum, we derive the continuum and we normalize the spectrum with respect to the continuum in such a way that the continuum has a normalized flux equal to 1 and we investigate the behaviour of spectral lines that in stellar spectra are mostly absorption lines. How do we quantify the information of the lines? Let’s start with the equivalent width. Measuring abundances: equivalent width Quantity for quantify the depth of the line. The equivalent width tells how much flux is absorbed for a specific line. The EW is the width for an absorption/emission line that is defined as the width of a rectangle whose height is equal to the height of the continuum, which is 1, and whose area is equal to the integrated area of the line. The equivalent width indicates the strength of a line, which is fundamental in deriving stellar abundances. It is a property which intrinsic of the line, it does not depend on the shape of the line and does not depend on the instrument. Moreover, it is not dependent on the rotation of the star. When a star rotates, the line is very broad, but the equivalent width is the same as if the star is not rotating. The equivalent width is connected with the abundance of the element. The curve of growth, illustrated on the right, describes the equivalent width of a spectral line as a function of the column density of the material from which the spectral line is observed. On the y axis we have the column density, on the x axis we have the EW. The line is the line that we use to derive the abundance of the gas that composes the stellar atmosphere. We can identify different regimes and slopes. We have a region where the increase of the ordinate is linear, then we have a saturation and then we have a region dominated by the wings of the line. Let’s look at it in more detail. – Weak line: it corresponds to the linear part of the plot, where the equivalent width (W) is proportional to the abundance of the elements (A). So in this part of the curve we derive a precise abundance determination because an increase of the EW corresponds to an increase of the abundance of the given elements. We are talking about lines in the spectrum that are weak, and the weak lines are better in deriving the chemical abundances than very strong lines. This is because W is proportional to the abundance of the elements. These are lines where the doppler core dominates the width of the line and the line is set by the thermal broadening. – Saturation: we have a plateau. It is a situation not convenient for deriving the chemical abundance. The doppler core reaches its maximum, this means that we have a saturation that is an increase/decrease in abundance of a give element that corresponds to 22 negligible variation of equivalent width. It is impossible to derive precise abundances in this regime of saturation where the EW is proportional to √log 𝐴. – Strong line: the lines are such that the wings of the lines dominate. The optical depth of the wings becomes significant → W α √𝐴. So if we look at the figure on the right we have that the weak like is at position A, then we have saturation in the circle and then we have strong lines where the wings of the line become important, in B. In B the strength of the line is strongly dependent on the gravity of the star. Strong lines are not so appropriate for deri