cogwiki: ForPraSternenhaufen

This is a rough draft and far from being finished. Feel free to add comments.

DISCLAIMER

This experiment is based on "Project 1: Colour-Magnitude Diagrams of Star Clusters" of The Open University and adapted to the setup as provided by the Campus Observatory Garching (COG).

General Introduction

This section should contain a general overview of astronomy (Stars, HRD, Star Clusters) and instrumentation (CCD, Mounting, Optics, Filters).

To the Stars!

What is a star? To some, the "obvious" answer is something like a, "huge ball of hot gas"¹. And from the point of view of the internal equation of state (EOS) (ideal gas of ions and electrons), for many stars on the Main Sequence, this statement is largely correct. But when we look at more massive Main Sequence stars, "a huge ball of hot gas" actually gives way to something more like a "huge ball of photons"; for, the EOS for massive Main Sequence stars is actually dominated by photon pressure, rather than ideal gas pressure.

Instrumentation

Errors and limitations (Seeing, Air mass, CCD-related errors,)

Star Clusters

Section 1.3 Background, which covers the following topics: star clusters, astronomical magnitudes and colours.

• Question: What are the two types of star clusters that are present in the galaxy and how do they differ from each other?

  Answer: Open clusters are loose collections of typically a few hundred stars, in the galactic disk. These clusters are generally young, with ages of a few million to a billion years old. Their stars belong to Population I. Globular clusters are tightly bound collections of typically a few hundred thousand to a million stars in the Galactic halo. These clusters are generally old with ages of a few billion years. Their stars belong to Population II.

As noted above, in this project you will obtain colour-magnitude diagrams (CMDs) of two open clusters and one globular cluster. Your aim will be to investigate the differences between the CMDs of these three clusters and explain these differences in terms of cluster ages.

You will also estimate the distances to the open clusters using the technique of main-sequence fitting.

>>> HRD Figure 1.1 <<<

A CMD plots the apparent magnitude of stars against their colour index, where an astronomical colour index is simply the difference between two magnitudes obtained through different filters. A CMD of a star is the observational analogue of a Hertzsprung-Russel diagram (HRD). On a HRD, absolute magnitude or luminosity is plotted increasing up the vertical axis (i.e. most luminous stars near the top) and spectral type or temperature increasing to the left is plotted on the horizontal axis (i.e. hottest stars on the left), as shown in Figure 1.1.

• Question: Why is it possible to replace absolute luminosity with apparent magnitude when studying a star cluster?

  Answer: All the stars are at roughly the same distance and suffer from the same amount of stellar extinction. Therefore the apparent magnitude, m, of all the stars is related to their absolute magnitude, M, by a simple offset, according to: M = m + (5 - 5 log₁₀(d/pc) - A) where d is the distance to the cluster and A is the interstellar extinction of the cluster in question. The absolute magnitude of each star in the cluster is proportional to the logarithm of its luminosity.

  Question: Why is it possible to replace temperature with a colour index such as (B-V) when studying a star cluster?

  Answer: Magnitudes obtained through different filters, such as B and V, sample different parts of the stars black-body like continuum spectrum. A difference between two apparent magnitudes is proportional to the ratio of two fluxes. Since all the stars are at the same distance, this is also proportional to the ratio of two luminosities in different parts of the spectrum. Since stars with different temperatures will have different spectra, they will also have different colours.

Hertzsprung-Russel diagrams and colour-magnitude diagrams are vital tools for understanding the evolution of stars and their composition. HRDs produced from theoretical calculations can be tested against observational HRDs to judge the accuracy of a particular theory. As you will see later, CMDs of star clusters can be used for distance determination purposes and also indicate the ages of different stellar populations.

Goals

The aim of this "advanced lab course" is to construct colour-magnitude diagrams (CMDs) for star clusters (open and globular clusters). The targets for the observation should be planned ahead of the observation. The analysis of the stellar clusters should reveal properties of the stellar population of the observed cluster. The analysis is conducted using a widely used, standard tool for image preocessing in astronomy, IRAF .

The objectives are:

• To prepare a schedule for the observations you want to do during the night. What calibration frames do you need? Choose observable star clusters (at least one globular and two open cluster) for this night.

• Obtain CCD images during the night for your objectes through at least two different broad-band filters and write a night log.

• Analyse your images by first creating a general correction frame for each filter (combined bias frames, dark frames and flat fields) and applying this correction to your images

• Perform psf photometry on the stars in each cluster to obtain their magnitudes and colours

• Produce a CMD for each cluster and discuss it (ages and distances)

Preperation

Before starting with the above objectives you should familiarise yourself with the important technical terms. You should be able to describe the telescope and its components. You should also be able to explain the physics connected to the objects you will observe.

This project is concerned with stellar photometry - that is measuring the apparent magnitudes of stars through one or more astronomical filters. The targets of observation are star clusters, which means that many individual stars of interest (typically tens or hundreds of stars) will be contained within each target image that you obtain. As well as obtaining images of the clusters themselves you will need to obtain appropriate calibration frames to correct for the bias signal and dark current, and to carry out a flat-field-correction.

However, in this project you will not be asked to measure standard stars in order to determine the extinction coefficient ε and zero-point offset ξ to calibrate magnitudes. Instead you will use a reference star of known magnitude in each target image, and determine the magnitudes of other stars relative to this reference point.

The quickest part of this project is likely to be actually taking the images of the star clusters. Planning the observations, including which targets to observe when, which calibration frames to take, etc. and analysing the data, are each likely to take far longer. It is therefore vital to plan how your group will carry out this project, including who will do what and when.

1.4 Preparing for observations:

Possible targets for your observation are shown in Table 1.1. The names of the clusters are given in the first column. 'M' indicates the designation of the cluster in Messier's Catalogue of cometlike objects, and 'NGC' its designation in the New General Catalogue of nebulae. The approximate right ascension (RA) and declination (dec) of the clusters are given in columns 2 and 3.

The fourth column lists the observing season in which it is appropriate to observe the clusters. Which three clusters you observe will depend on the time of year you are at the observatory. The fifth and sixth columns list the constellations in which the clusters lie and their approximate diameter in arcminutes.

The final column indicates the previously measured interstellar extinction to the cluster, to which we shall return later.

As a first task you have to find suitable objects for the night. Keep in mind that the night sky changes with season and also during a night, objects rise and set again. The following criteria should be met by the objects you choose:

• the objects should be visible between dusk and midnight, which should be the time frame for the observations
• choose objects with minimal airmass (high declination)

• Get E(B-V)

You should prepare a time schedule for your observations including taking calibration frames. At this point you should talk to your tutor and discuss your schedule and a date for the observation.

Observation

This section is concerned with the actual observation. The experiment will start during early evening before dusk. You will open the dome of the telescope and startup all the equipment that is necessary for the observation (How to startup?). You can get used to the handling of the telescope or even do some observations with the Hα-filter during daylight.

During dusk you will take your flat fields for all the filters. You will use a different program during for this Details.

Begin by starting up the MaximeDL software. MaximeDL is a software for controlling telescop and all the connected devices. It has also data analysis capabilities. However, we will only use it for operating the telescope and taking the desired exposures.

A typical observational cycle will start with an entry in the night log.

• Adjust focus
• Observe an object and check maximum count, avoid saturation
• Start observational sequence for this object
• Continue with other objects including standard field

Following is taken form 1.5 Data taking

For each cluster you will need to obtain two images, or sets of images: one through the B-Filter and one through the V-Filter ( We don't use Johnson filter). The integration times you use will be long enough that faint stars are detected, but not so long that your reference stars saturate the detector ( We won't use reference stars, but a standard field calibration?), or the field drifts significantly during the exposure ( not relevant for our telescope, but can be checked by looking at the raw images). You may want to experiment with exposures 5 s, 10 s and 30 s for instance. You can also average multiple images of the same field to obtain longer effective exposure ( Sentence should be adopted to our setup). Don't worry if 3 or 4 of the brightest stars in the image are saturated - you can look up the magnitudes of these bright stars at CDS - it is far more important that the majority of the stars are adequately exposed and that your 9th and 10th magnitude reference stars are not saturated ( Same with this sentence). To make the data reduction easier, it is simplest if all your images through the same filter have the same exposure time ( True for IRAF?).

It is good practice to obtain bias frames and dark frames before and after your target observations, or interspersed between them. Also, it is most convenient if your dark frames have the same exposure times as your target frames, as this saves having to scale them later.

Remember that you will need to take flat fields through each of the filters during dusk.

As you obtain each target image or calibration frame, verify that it is adequate for its purpose by quickly examining it on screen. If the image drifts during exposure (which should never happen with our telescope), if the stars you are interested saturate, if they are underexposed, or the image is otherwise unsuitable, then repeat the observation until you obtain one that is satisfactory. When you have a suitable image make sure you save the file and note down the details in your observing log. ( This is true if we use MaximeDL, but might be different with ACP. A decision should be made.)

Analysis

Section 1.7 will be basis for this part (needs adjustment HRD instead of CMD. there is a decision to make depending on the amount of work connected to the calibration to a standard field.)

As noted above, a CMD is usually plotted with apparent magnitude increasing downwards and colour index (B-V) increasing to the right.

Figure 1.2 or some adaptation (HRD instead of CMD)

• Question: If a CMD contains stars falling on the track shown in Figure 1.2a, what can you say about how the temperatures of the stars vary with their apparent brightness?

  Answer: Apparent magnitude, V, increases downwards, so the stars' apparent brightness upwards. The value of the colour index (B-V) increases towards the right, so stars on the left have a numerically smaller value of (B-V) than stars on the right. In other words, stars on the left have a smaller difference between their B and V magnitudes than stars on the right. This could be due to a numerically smaller B value or a numerically larger V value. So, stars on the left must be relatively brighter in B or fainter in V, when compared with stars on the right. Since the B magnitude (blue) is measured at shorter wavelengths than the V magnitude (green-yellow), stars that are relatively brighter in B or fainter in V are hotter.

So a smaller numerical value in (B-V) indicates a hotter star.

Considering the track shown in Figure 1.2a, the brightest stars are hotter than the fainest stars.

• Question: If a CMD contains stars falling on the track shown in Figure 1.2b, what can you say about how the temperature of the stars varies with their apparent brightness?

  Answer: Following a similar argument to that outlined above , the track shown in Figure 1.2b indicates that the brightest stars are cooler than the faintest stars.

In fact the track shown in Figure 1.2a follows the trend that is seen in the main sequence whereas the track shown in Figure 1.2b follows the trend that is seen in the giant branch (post main-sequence evolution).

When a star cluster is born, its initial CMD will show all its stars to lie on the main sequence. The most most massive stars are hotter (i.e. bluer) and brighter and lie at the top of the main sequence; the least massive stars are cooler (i.e. redder) and fainter and lie at the bottom of the main sequence. As stars age, they move off the main sequence onto the giant branch.

• Question: Which stars will move off the main sequence first?

  Answer: The most massive stars evolve more quickly. So the first stars to move off the main sequence will be the hotter (i.e. values), brighter ones.

For a given star cluster, depending upon its age, parts of both the main sequence and the giant branch may be visible in its CMD (as shown in Figure 1.3). The upper point of the main sequence that is populated by stars is called the main-sequence turnoff. Above this point, almost all the stars have evolved off the main sequence onto the giant branch. The position of the main-sequence turnoff therefore indicates the age of the cluster.

Figure 1.3 (good, but maybe use a HRD from Wikipedia?)

• Question: In general terms, how do the CMDs that you have obtained differ from that shown in Figure 1.3?

  Answer: Your data have a limiting magnitude that is much brighter than that shown in Figure 1.3, i.e. there will be a limiting magnitude (possibly around magnitude 14 or 15) below which you detect no stars. This means that some part of the CMD will not be visible to you. You may only see the giant branch, or the upper part of the main sequence for instance (/!\ we will see what our setup gives us).

Identifying the main sequence and the giant branch

Using the information above regarding how the colours of the star should vary with their magnitude on the main sequence and on the giant branch.

• Task For each of the CMDs that you have constructed, can you identify the main sequence? Can you identify the giant branch? Where they are visible, sketch in the positions of the main sequence and giant branch on each of your CMDs. Can you identify any likely interloper stars on your CMDs that may not belong to the clusters?

Discuss your answers with your tutor before moving on.

== Distances to star clusters ==

There is more to do.

Ages of star clusters

Log on to your account on the Linux machine via VNC. The tutor should have copied the raw images to your working directory. It is useful to produce a local backup in case you need to start over.

INTERNAL_USE_ONLY_open_university_clusters.pdf INTERNAL_USE_ONLY_open_university_observatory_manual.pdf