Astrophysikalisches Praktikum Multi Wavelength Studies of the

Document Sample
Astrophysikalisches Praktikum Multi Wavelength Studies of the Powered By Docstoc
					                   a                 u
          Universit¨ts - Sternwarte M¨nchen

      a u                                           a
Fakult¨t f¨r Physik der Ludwig Maximilians Universit¨t




         Astrophysikalisches Praktikum


       Multi-Wavelength Studies of
     the Coronet Star Forming Region




             Prof. Dr. Thomas Preibisch

                Dr. Thorsten Ratzka
1     Introduction
Stars are the fundamental building blocks of the baryonic universe. Therefore, the process of star
formation is of utmost importance for astrophysics.
In this exercise, X-ray, optical, and infrared data of a young stellar cluster will be analyzed. The
aim is to compile a list of cluster members by identifying the X-ray sources detected in a deep
observation with the Chandra satellite in infrared images from the 2MASS survey and the Spitzer
space telescope. The infrared data are then used to obtain information about the evolutionary
state and the circumstellar disk properties of the population of young stars.

1.1   Outline of low-mass star-formation and pre-main sequence evolution
Stars are born in the dense, cold cores of molecular clouds. The inside-out gravitational collapse
of a rotating cloud core leads to the formation of a so-called protostar on a time-scale of about
10 000 years. The infall of high angular momentum gas forms a spinning, circumstellar disk
through which most of the star’s final mass spirals onto the protostar. During the first 100 000
years, these protostars are embedded within dense cocoons of dust and gas, and are mostly hidden
from view at visible wavelengths. Infrared light, from wavelengths of a few microns upwards, can
pierce through the dusty veil and provide a peek at such very young, newborn stars.
After a few 100 000 years, the material in the dense circumstellar envelopes is dissolved; some
part of this material gets accreted onto the star (usually via a circumstellar disk), another part is
blown away by the radiation and winds of the young star. This dispersal of the envelopes makes
the young objects directly visible in optical light. At an age of about 106 years, most young
stars are surrounded by relatively flat circumstellar disks, from which they continue to accrete
material. Since these disks are also the site where planets may form, they are often denoted as
protoplanetary disks. When the accreted material hits the stellar surface it produces a hot shock
zone which gives rise to strong Hα emission. Young stars with circumstellar accretion disks are
called classical T Tauri Stars (CTTS).
As described below in more detail, these disks evolve and are dissipated on timescales of several
million years. As the accretion rates decrease, the Hα emission gets weaker and finally disapears;
young stars with weak or no Hα emission are therefore called weak line T Tauri stars (WTTS).
Finally, after periods between a few 10 million years (for stars with about solar mass) and a few
100 million years (for stars with less than ∼ 1/3 of a solar mass) the stellar contraction has heated
the centers of the stars to sufficiently high temperatures to start hydrogen fusion processes, and
the stars begin their main phase of life as main sequence stars.

1.2   Empirical classification of young stellar objects by their spectral energy dis-
      tribution
The evolution of young objects from the protostellar phase to the main sequence is also traced by
characteristic changes in the broad-band spectral energy distribution (SED), i.e. the distribution
of the observed flux from UV wavelengths to the radio bands.
The deeply embedded protostars are completely invisible in the optical regime. All but the longest
wavelength (far-infrared to radio) radiation from the central star is completely absorbed in the
dense dusty envelope. The dust particles, that are heated by absorbing the radiation from the host
star and by viscous dissipation of gravitational energy, re-emit their energy at mid- to far-infrared
wavelengths. The observed SED shows a broad peak in the mid- to far-infrared regime, starting

                                                 1
at wavelengths of a few µm. Such an SED is denoted as class I SED. This classification scheme
is based on the slope of the SED between near-infrared (∼ 2 µm) and mid-infrared (∼ 10 µm)
wavelengths, as described below in more detail.
In classical T Tauri star systems, the central young stellar object is usually directly visible in
optical light. The dusty disk, which is now mainly heated by absorbing radiation from the host
star, radiates at infrared wavelengths. The SED from the star and disk system thus usually shows
a peak at optical wavelengths (stellar light), but at longer wavelengths the infrared emission
from the dusty disk produces a second peak, the so-called infrared-excess. SEDs of this kind are
denoted as class II SED.
In the weak-line T Tauri star systems, the infrared excess from any remaining disk material is very
weak or entirely absent. The SED of the WTTS is thus dominated by photospheric emission from
the young stars (just like the Sun) with no or at most very weak infrared excesses. Such an SED
is denoted as class III SED.


1.3   Temporal evolution of circumstellar disks
                                                                  Circumstellar disks around young
                                                                  stars are a common feature of
                                                                  stellar evolution and of planetary
                                                                  system formation. These disks
                                                                  supply a reservoir of gas and
                                                                  dust from which planets may
                                                                  form. They are also directly in-
                                                                  volved in the formation and colli-
                                                                  mation of jets and outflows, gen-
                                                                  erally thought to be implicated
                                                                  in the key process of angular mo-
                                                                  mentum removal.
                                                                  The dust in primordial proto-
                                                                  planetary disks is mainly heated
                                                                  by absorbing radiation from the
                                                                  host star.      The dust closest
                                                                  to the star is the warmest and
                                                                  dust particles get progressively
Figure 1: The spectral energy distribution for various stages of cooler towards the outer edges
young stellar evolution.                                          of the disk. The warmest (T ∼
                                                                  1000 K) dust particles in the in-
nermost disk regions produce excess emission at wavelengths of a few µm, while the much cooler
dust in the outer parts of the disk radiate mainly at far-infrared wavelengths (around 100 µm).
Such protoplanetary disks thus produce a strong infrared excess starting already at near-infrared
wavelengths.
In these disks, planets form like snowballs over millions of years, as small dust grains clump
together to form larger bodies. Some of these cosmic rocks then smash together to form rocky
planets, like Earth, or the cores of gas-giant planets like Jupiter. Large rocks that don’t form
planets often become asteroids and comets. As these rocky structures violently collide, bits of
dust are also released back into space.

                                                 2
Planetary debris disks represent a later stage of evolution, with most of the gas having been
dissipated. These disks are comprised mostly of small dust grains presumably formed from colli-
sions between small planetesimals and larger rocky bodies. Since these evolved debris disks contain
much smaller amounts of dust than the younger protoplanetary disks, the infrared excesses caused
by them are much weaker. Furthermore, as most of the remaining dust in the evolved disks it
at rather larger distances from the star and thus rather cool, the excess emission is restricted to
longer wavelengths (> 10 µm).
In 2–10 Myr, the optically-thick young disks lose their original gas and dust through accretion
onto the central star or through agglomeration and accretion to form planets and planetesimals.
This transition between young, optically-thick, gas-dominated disks and older, residual dust debris
disks is crucial to our understanding of the planet formation process. By observing disks of various
ages, one can trace the evolution of a formless cloud of dust and gas into a mature system of
planets.


1.4   Detection of infrared excess in the color-color diagrams
The complete characterization of the SED of a young stellar object requires observations at a very
wide range of wavelengths, from the optical to the millimeter regime. However, for the detection
and (rough) characterization of infrared excesses, observations at a few selected wavelengths are
often sufficient. A widely used set of wavelengths consists of the J- (1.2 µm), H- (1.6 µm),
and K-band (2.2 µm), where near-infrared photons can pass through the earth’s atmosphere.
Measurements of the magnitudes in these bands then allow to determine near-infrared colors. For
a quantitative analysis, the observed objects are plotted into a color-color diagram (Fig. 2).
                                                                  As the color-color relationships
    3.0                                                           of main sequence stars are well
                                                                  known, a theoretical main se-
    2.5                                                           quence can be plotted for refer-
                           ag




                                                                  ence. In Fig. 2, the colors for
                         m
                      10




    2.0                                                           main sequence stars are shown
                   V =




                                                                  by the solid line, those of giant
                   A




    1.5                                                           stars by the dashed line. The
J-H




                                                                  effect of interstellar dust extinc-
    1.0                                                           tion is also well understood. The
                                                                  reddening vector is drawn as an
    0.5                                                           arrow in Fig. 2. This allows
                                                                  bands to be drawn on a color-
    0.0                                                           color diagram defining the region
                                                                  in which stars reddened by in-
   -0.5                                                           terstellar dust are expected to
      -0.5        0.0        0.5        1.0        1.5       2.0 be observed (the dotted lines in
                                  H-K
                                                                  Fig. 2). The typical axes for in-
           Figure 2: Near-infrared color-color Diagram.           frared color-color diagrams have
                                                                  H −K on the horizontal axis and
J − H on the vertical axis. On a diagram with these axes, stars located to the right of the main
sequence and the reddening band are significantly brighter in K, the longest wavelength band,
than main sequence stars or stars which have experienced reddening due to dust. This means that

                                                 3
young stars, which exhibit excess radiation at longer wavelengths, will occupy a distinct region in
color-color diagrams. By plotting stars on a color-color diagram, it is possible then to see what
stage of stellar evolution a star is in by looking at its position on the diagram. Stars located
within the reddening band (plotted by green symbols in Fig. 2) show no evidence for infrared
excesses and may represent redenned main sequence stars. The stars located below the reddening
band (marked by red symbols in Fig. 2) show infrared excesses and thus evidence for circumstellar
matter.
Since we cannot watch the evolution of individual stars, studies of large samples of young stars
with different ages can provide us with important information about the evolution. The timescale
for the disk evolution is different from star to star. For example, there is evidence that the disks
around solar-mass stars dissolve faster than disks around lower-mass stars. But the evolution of a
disk also depends on the environment, e.g., the strong UV radiation of nearby massive stars can
photoevaporate the disk of a young star and dissolve it on very short timescales.
Considering the full young stellar population of a specific region, the fraction of stars that display
infrared excesses decreases with the age. Typically, at ages around 3 Myr, half of the stars show
no longer their infrared excesses, i.e. have substantially cleared their (inner) circumstellar disks.


2    Star clusters and associations
During the last decade, observations have shown that most stars do not form in isolation, but in
clusters. While some young clusters consist of only a handful of stars, others (such as the famous
Orion Nebula Cluster) contain several thousand members. The typical sizes of such clusters range
from a few tenths of a parsec to several parsecs.
While most young stellar clusters are initially gravitationally bound, this changes as soon as the
winds and the radiation from the newly formed stars remove the remaining gas from the young
cluster. Once the gas is dispersed, most clusters are no longer gravitationally bound and thus
constitute open clusters. The largest and particularly loose clusters are denoted as associations,
that often extend over tens of parsecs. Most of these clusters and associations disperse on
timescales ranging from 3 to 40 Myr.
Many details of the processes involved in stellar cluster formation remain unexplained. Particularly
important questions are: Do all members of a cluster form at the same time, or one after the other
over a long period of time? Is the mass distribution of the newly formed stars, the initial mass
function (IMF), universal, or does it vary with either environment or time. How is the evolution
of the young stars and their protoplanetary disks affected by their neighborhood and how does it
depend on the stellar mass. Before one can address questions like these, one needs an (at least
statistically) complete sample of the cluster members.
Therefore, the obvious first step is to identify the young stellar members of a star forming region.
While this sounds trivial, it is in fact often very problematic. The members of an open cluster
are often dispersed over quite large regions in the sky, often many hundred square arcminutes.
The young stars in associations such as the Taurus-Auriga association are even spread out over
nearly 100 square-degrees on the sky. This loose configuration of many young clusters (see, e.g.,
Fig. 3) and associations makes it very difficult to discern cluster members from unrelated fore-
and background stars, the so-called field stars, that appear just by chance in the same region of
the sky. In fact, most stars one can see in the field of nearby open clusters and associations are
actually completely unrelated older field-stars in the background.

                                                 4
Figure 3: The famous “double cluster” h and χ Per. Both open clusters reside at a distance of
about 2 kpc within the Galactic plane, and therefore many of the stars visible in the image are
unrelated galactic field stars.


Observational surveys capable of detecting the entire range of stellar masses and ages present
within a cluster are therefore needed if one wants to study the properties of young clusters.
Infrared excess emission is a good and widely used tracer to distinguish member of a young stellar
cluster from unrelated, much older, field stars. However, searches for infrared excess objects
systematically miss those young stars that have already depleted their disk and do no longer show
detectable infrared excess. Samples of young stars selected by infrared excess thus suffer from a
strong bias against diskless young stars, although these may have the same ages as the infrared
excess stars. This bias has very serious consequences for any studies of the distribution of stellar
masses or stellar ages in the cluster.
Any meaningful study of the stellar population of star forming regions thus requires an unbiased
census of the young stellar populations. For this, an alternative tracer for young stars, independent
of circumstellar disks, is needed. As described in the next section, X-ray emission provides such
a tracer.


3    X-ray emission from young stars
Stars of almost all kinds emit some fraction of their luminosity as high-energy X-ray radiation. A
look at the Sun allows to directly see where this X-ray emission comes from. The solar corona,
i.e. the outermost part of the solar atmosphere, contains hot plasma at temperatures of up to a
few millions of degrees. Since in the corona the shape and character of the hot gases are controlled
by the solar magnetic fields, there is a clear relation between the magnetic structure and the X-ray

                                                 5
bright areas. Many structures in the corona have a filamentary (or thread-like) appearance which
seems to link two regions. These filamentary structures are called coronal loops. In general, the
loops are hotter and denser than the areas around them. They are thus brighter in X-rays.
                                The total X-ray energy output of our Sun (and of other solar-like
                                main sequence stars) is quite small: only one part in a million of the
                                total luminosity is emitted in the X-ray band (LX /Lbol ∼ 10−6 ).
                                When the first X-ray observations of young stellar clusters were
                                obtained some 30 years ago, the researchers were very surprised to
                                find that young stars generally show much stronger X-ray emission,
                                hundreds to thousands times stronger than that of our Sun.
                                The physical mechanisms that lead to the X-ray emission and their
                                relation to the stellar magnetic activity are not yet fully understood.
                                A number of relationships between X-ray and other stellar proper-
                                ties are found. Most evidently, the X-ray luminosity LX scales
Figure 4: The Sun in X-rays.
                                roughly linearly with the stellar bolometric luminosity Lbol . This
relationship is frequently summarized as a constant ratio LX /Lbol , where the exact value lies typ-
ically at log (LX /Lbol ) ≈ −4. LX is also correlated with stellar mass, photospheric temperature,
stellar radius and rotation. The average T Tauri X-ray luminosity appears to be constant with
age during the first 10–100 Myr.
The astrophysical origins of these relationships are poorly understood, and it is unclear which
represent causal links rather than ancillary statistical dependencies. The only relation expected
from standard magnetic activity theory is between LX and some rotation indicator, reflecting
more powerful magnetic dynamos in rapidly rotating convective stars, and a link between X-ray
surface flux and X-ray temperature, which is expected from standard solar-type magnetic loop
flare models. It is possible, for example, that the LX –mass correlation represents a fundamental
connection between surface activity and the incorporation of fossil magnetic fields from the star
formation process. The dissipation of such fields by ohmic and turbulent decay can be sufficiently
slow that they may be present throughout the T Tauri phase.


X-ray activity as a tracer of young stars
In addition to opening a new window into the astrophysics of young stars, X-ray surveys can serve
as a powerful tool for finding previously missed young stellar objects and studying their properties.
The strong X-ray activity of young stars (up to ∼ 50 million years old) offers a particularly effective
way to discriminate the members of young clusters from unrelated, much older field stars. X-rays
are equally sensitive to young stars which have already dispersed their circumstellar disks, thus
avoiding the bias introduced when selecting samples based only on infrared excess.
Therefore, X-ray observations are a very important tool to reveal the complete stellar populations
of star-forming regions. Since X-ray radiation is much less affected by extinction than optical
light, X-ray observations can penetrate up to extinctions of AV ∼ 500 mag into dark clouds and
allow a deep look at embedded very young stellar objects (protostars).
Such an unbiased census of the young stellar populations in different star forming clouds is essential
in addressing a variety of important issues concerning star formation and pre-main sequence
evolution. The combination of deep X-ray observations with sensitive near-infrared data has
recently greatly advanced our knowledge of the stellar populations in many star forming regions.
Only if the census of all young stars from a given cloud is reasonably complete, then the cloud’s

                                                  6
                   Figure 5: Optical image of the R CrA star forming region.


star formation history, mass function and other key properties can be established reliably.


4    The Corona Australis star forming region
With a distance of only 130 pc the Corona Australis star forming region is one of the nearest
(about 3.5 times closer than the Orion Nebula Cluster) and most active regions of recent and
ongoing star formation. It consists of a highly elongated system of dark molecular clouds with
six condensations. The region contains a loose cluster of a few dozen known young stellar
objects, which cover a wide range of masses (from intermediate-mass Herbig Ae/Be stars down
to very low-mass brown dwarfs) and evolutionary stages (from pre-stellar cores through class 0
and class I protostars, class II T Tauri stars, to class III objects that have already cleared their
dusty environment). The complex has a centrally-condensed molecular cloud core (“condensation
A”) centered near the bright star R Coronae Australis. This core measures more than one by two
light-years (0.4 by 0.7 parsecs) in extent and contains about 50 M of molecular gas. It contains
the densest clustering of very young, embedded objects, which is known as the Coronet cluster.
Many of the young stellar objects in the extended R CrA region are optically visible and have
typical extinctions of AV ∼ 3 mag. Most of the young stellar objects in the central dark cloud,
however, are deeply embedded in this cloud and suffer from extinctions ranging from AV ∼ 10 mag
to more than AV ∼ 50 mag.

                                                 7
5     Observational Data
In this exercise we will utilize observational data of the Coronet cluster obtained with the Chandra
X-ray satellite observatory, optical images from the Digitized Sky Survey, near-infrared images
from the 2MASS survey, and near- to mid-infrared images obtained with the Spitzer infrared
space telescope.

5.1   Chandra X-ray data
The Chandra X-ray observatory is a NASA mission. It was launched in the year 2000 and orbits the
earth in a strongly elliptical orbit. Chandra is sensitive to X-rays with energies between ∼ 0.2 keV
and ∼ 10 keV. The data were collected with the Advanced CCD Imaging Spectrometer ACIS
in its imaging configuration. The ACIS-I detector consists of four abutted CCDs, giving a total
field-of-view of 17 × 17 . Due to the extremely high quality of Chandra’s X-ray telescope mirrors,
it provides a very good spatial resolution: the full-width at half maximum of the point spread
function is less than 1 in the center of the field. The pixel size of the ACIS CCDs is 0.5 × 0.5 .
The Chandra data of the Coronet cluster were obtained in 2003. The total exposure time was
38 126 seconds, i.e. 10.6 hours. The total number of X-ray photons detected in this observation
is 83 424. Modern X-ray detectors as those onboard of the Chandra X-ray observatory detect
individual X-ray photons. Each single X-ray detection constitutes a so-called event. A very
favorable property of X-ray detectors is that they can not only measure the position of the
incoming photon on the detector (i.e. the direction from which the photon arrived), but also the
arrival time and the energy of each event. The basic data product of an X-ray observation is
the so-called event-list, that stores the position, energy, and arrival time of each event in a table.
This event list is the basis for the creation of observation products such as images, spectra, and
lightcurves. Binning the event list with respect to x and y detector coordinates yields an image.
Binning the events in a selected region of the detector by their respective event energies yields
the spectrum of any source in this region. Binning the events in a selected region of the detector
by their respective arrival times yields the lightcurve of any source in this region.

5.2   Near-Infrared Data from the Two Micron All Sky Survey (2MASS)
The Two Micron All Sky Survey has uniformly scanned the entire sky in the three near-infrared
bands J (1.25 microns), H (1.65 microns), and K (2.17 microns) to detect and characterize point
sources. 2MASS used two highly-automated 1.3-m telescopes, one at Mt. Hopkins, Arizona, and
one at the Cerro Tololo Inter-American Observatory (CTIO), Chile. Each telescope was equipped
with a three-channel camera, each channel consisting of a 256×256 array of HgCdTe detectors,
capable of observing the sky simultaneously in the three bands.
The main 2MASS Data Products are (1) a digital atlas of the sky, and (2) a point source
catalog containing accurate positions and fluxes for about 300 million stars and other unresolved
objects. The 2MASS magnitude limits (for SNR=10) are mJ = 15.8 mag, mH = 15.1 mag, and
mK = 14.3 mag.

5.3   Near- to Mid-Infrared Data from Spitzer
The Spitzer Space Telescope carries an 85-centimeter cryogenic telescope and three cryogenically
cooled science instruments capable of performing imaging and spectroscopy in the 3.6 to 160 µm

                                                  8
           Figure 6: The Coronet cluster as seen with the Spitzer space telesecope.


range. Here, we will use data that have been obtained with Spitzer’s wide field, broadband
imaging instrument called Infrared Array Camera (IRAC). IRAC is a four-channel camera that
provides simultaneous 5.2×5.2 arcminutes images at 3.6, 4.5, 5.8, and 8.0 µm. All four detector
arrays in the camera are 256×256 pixels in size, with a pixel size of 1.2”×1.2”.




                                              9
6     Analysis
6.1   Produce an X-ray image from the event list
The software package created for the analysis of Chandra data is called CIAO. To start CIAO
simply type ciao on the command line.
The first step in the analysis is the creation of X-ray images from the event lists. The command
for this task is dmcopy. The arguments of the command are the desired spatial binning factor
(i.e. how many 0.5 × 0.5 detector pixels are combined for each image pixel) and, optionally,
constraints of the energy and/or arrival times of the selected events. Since we want to use the
full information collected over the entire exposure time, we do not apply any temporal selection
criteria. Regarding the event energy, we select only events with energies between 0.2 keV and 8
keV, because events at lower and higher energies are significantly contaminated by cosmic rays
and/or the charged particle background.
To create an image of the full observed field-of-view (detector pixel coordinate values, x,y, range
from 2600 to 5600) in which one image pixel is identical to one detector pixel, type the command

      dmcopy ”chandra.fits[X=2600:5600,Y=2600:5600][energy=200:8000][bin x=1,y=1]”
      chandra-bin1.fits

In a similar way, images with a pixel binning factor of 2 and 4 can be created with the commands

      dmcopy ”chandra.fits[X=2600:5600,Y=2600:5600][energy=200:8000][bin x=2,y=2]”
      chandra-bin2.fits

and

      dmcopy ”chandra.fits[X=2600:5600,Y=2600:5600][energy=200:8000][bin x=4,y=4]”
      chandra-bin4.fits


Action 1: Create images with a binning factor of 1, 2 and 4.



6.2   Inspection of the X-ray image
The tool we will use for the inspection of the resulting images is the SAOImage DS9 astronomical
imaging and data visualization application. It is started from the command line by typing:

      ds9 chandra-bin1.fits

To optimize the display, try the following parameters:

    • title bar: Scale → Scale Parameters, enter the values Low=0 and High=10 and click Apply

    • middle bar: color → heat

    • middle bar: scale → square root

    • middle bar: Zoom → - and +

                                               10
The leftern small image above the main image display shows the full image extent and the currently
shown field in the main display is indicated by a blue box (Fig. 7). The blue box can be shifted
with the cursor to change the region shown in the main display. The right small image above the
main image display shows an enlargement of the image region around the current cursor position.
When the cursor is in the main image display, the boxes in the upper left part of the window give
the following informations:

   • Image numbers show the cursor/pixel position relative to the bottom left corner;

   • FK5 α and FK5 δ numbers show the right ascension and declination of the cursor/pixel
     position;

   • the Value number shows the photon count at the cursor/pixel position;

   • if one selects Pixel Table in the menu Analysis a table displays the Value numbers of the
     surrounding pixels.


Action 2: The brighter X-ray sources are easily identified in a visual inspection of the image.
Inspect a few bright X-ray sources near the center of the image. Use Analysis → Pixel Table to
estimate the Full-Width-Half-Maximum of the Point-Spread-Function. Is the FWHM constant
over the whole field of view?



6.3   Comparison with an Optical Image
Now we want to find out where the most prominent X-ray sources are located in the star-forming
region and how their optical counter-parts look like.




                            Figure 7: Screenshot of the ds9 window.

                                               11
After clicking in ds9 in the menu bar on Frame → New Frame and selecting Tile Frames in the
same sub-menu an empty frame appears right of the Chandra image. Click now in the empty
frame and open the file dss-red.fits. This optical image has been taken from the red plates of the
Digitized Sky Survey and shows the same region as the Chandra image.



Action 3: Can you identify the brighter X-ray sources in the optical image? Do they have a
special appearance? Note the coordinates of at least five X-ray bright sources. Is the star R CrA
(α =19h 01h 53.7s , δ =-36◦ 57’08”) visble in the X-Ray image?



6.4   Determination of the background level
The detectability of faint sources is limited by the background level in the X-ray images. The
background originates mainly from the particle background and the diffuse X-ray background
emission. In order to estimate the detection limit, one has to determine the mean background
level (counts/pixel) in a region free from (bright) X-ray sources. The command dmstat allows to
determine the number of counts within a specified region. For example, the command

      dmstat ”chandra.fits[sky=circle(3735.0,3929.0,100.)][energy=200:8000]” centroid=no

reports that the circular region with a radius of 100 pixels centered at the pixel position x=3735.0
and y=3929.0 contains 227 counts.



Action 4: Use this value, to compute the mean background in units of counts per square-
arcseconds. Do other regions exhibit the same number of background counts?



6.5   Computation of the detection limit
The most critical part in any source-detection procedure it to decide whether an observed clus-
tering of counts at a specific image location is due to the presence of an X-ray source or just
a random fluctuation of background photons. While it is very easy to spot the relatively strong
sources in the X-ray image, one is often interested in the faint sources and thus would like to have
a reliable and objective criterion to discern between a faint source and a background fluctuation.
A very simplified approach is the definition a small region called “detect cell”, for which one then
compares the number of observed counts to the statistical fluctuations of the background counts
(the statistics of the background is usually determined from a much larger area). Since the FWHM
if about 1.5”, a good choice for the size of the detect cell is 3”×3”. From the background values
determined above, the expected number of background counts in such an area is 0.260 counts.
The nature of the X-ray background (random positions for independently detected single photons)
implies that the background counts should obey the Poisson statistics. In this case, the probability
Pλ (k) that k counts are detected when the expected number of counts is λ is given by the formula

                                                   λk −λ
                                        Pλ (k) =      e .                                       (1)
                                                   k!

                                                12
Action 5: Use the expected number of background counts per detect cell determined above to
compute the probability that a single detect cell contains 0, 1, 2, 3, 4, 5, 6, or 7 counts as a result
of random background fluctuations.

The probability that fluctuations of the background produce up to n counts in the detect cell is
given by

                                                    k=n
                                       Pλ (≤ n) =         Pλ (k) .                                 (2)
                                                    k=0
From this, it follows that the probability to find n or more counts in a detect cell as a result of a
background fluctuation is given by

                                                       k=n
                                     Pλ (≥ n) = 1 −          Pλ (k) .                              (3)
                                                       k=0


Action 6: Compute this probability for n = 3 . . . 6.

From these considerations, it is clear that the probability to see more than about 3 counts in a
detect cell as a result of random background fluctuations is very low, and decreases quickly with
the number of observed counts.
Now we need a criterion to statistically discern between random background fluctuations and
a “significant source detection”. However, the choice of the probability limit is quite delicate.
Using a rather high limit (in terms of detected counts, i.e. a very low probability that the detected
number of counts is due to background fluctuations) results in a very reliable source list, i.e. no
false detections, but at the cost that many weak sources remain undetected. Using a rather low
limit allows one to detect very faint sources, but at the cost of accepting a serious number of
false-detections.
One way to establish a useful limit is to consider the whole detection process as a series of many
repeated detection experiments. Dividing the total area of the X-ray image by the size of a single
detect cell can then be considered as the “number of repetitions” of the detection experiment.
Multiplying this by the above determined false-detection probability yields the expected number
of “false-detections”.

Action 7: Determine the detection threshold (in units of counts per detect cell) for which one
would expect roughly one “false-detection” in the entire image.



6.6    Source detection
Above we identified X-ray sources by eye. A more convenient, efficient, and objective way to
detect X-ray sources is to use a specially designed routine within ciao:

      wavdetect chandra-bin1.fits sources.reg cells.fits sources.fits background.fits scales=“2
      4 8 16” falsesrc=0.1

This routine does not only use the number of counts in detect cells, but also considers other
important aspects such as the spatial distribution of a source, e.g., for a point-like source one

                                                  13
would expect to see a peak in the spatial distribution of counts, which is surrounded by decreasingly
weaker wings. The routine also uses different scales for the detection and the user can specify
the number of false detections per scale per image with the parameter falsesrc. Moreover, the
program generates a source cell image (cells.fits), a reconstructed source image (sources.fits),
and a normalized background image (background.fits). The detected sources are listed with their
position and size in the file (sources.reg).

Action 8: How many sources is the program detecting? Discuss the origin of the structures
visible in the normalised background image. Since the detection routine needs about 5-10 min,
we can meanwhile go the next step.



6.7   Computation of the mass detection limit
The detection limit of 4 counts per source is now used to estimate the minimum detectable X-ray
luminosity of a source in the target cluster.
Using reasonable assumptions about the spectrum of the sources (in this example, emission
from a thermal plasma with temperature T = 107 K and an extinction corresponding to AV =
3 mag), the calibration data for the Chandra detectors tell us that an incoming X-ray flux of
10−10 erg/sec/cm2 (measured directly in front of the satellite) produces a source count rate of
4.33 cnts/sec.

Action 9: Use these numbers in combination with the detection limit (4 counts), the exposure
time of the X-ray image (38 126 sec), and the distance to the Coronet cluster (130 pc) to compute
the corresponding X-ray luminosity.

From many studies of the X-ray emission from young stellar objects it is well established that
the X-ray luminosities are correlated with the bolometric luminosities, roughly following the re-
lation LX ∼ 10−4 Lbol (we ignore here that there actually is a considerable scatter around this
correlation).

Action 10: Use this relation to estimate the minimum bolometric luminosity of young stars that
should be detected as X-ray sources.

The table pms-models.pdf lists the bolometric luminosities for 1 Myr old stars of different masses.

Action 11: Use this table and the above determined limiting bolometric luminosity to estimate
down to what stellar mass one can expect to detect the young stars in the X-ray image. Based on
the PMS table, estimate the mass limit of objects that are detectable with 2MASS for AV =3 mag,
10 mag, and 30 mag.



6.8   Inspection of the source list
To overlay the detected sources on the Chandra image choose Load Regions from the menu
Region while the image is displayed and load the file sources.reg created before. Each detected
source is now represented by a green ellipse. To save the source list in equatorial coordinates

                                                 14
(RA and DEC) rather than in detector pixel coordinates, go again to the Region menu and set
File Coordinate System to WCS and Equatorial J2000. In the File Coordinate System menu, also
choose whether you want the output in degrees or sexagesimal (used in this example). Finally, in
the Region menu select Save Regions and select as filename source-wcs.reg1 . Now, load the DSS
image, the 2MASS images, and the Spitzer images and overlay the source list on them.

Action 12: How many X-ray sources have counterparts in the optical DSS image? How many
counterparts can be found in the 2MASS images and how many X-ray sources are detectable in
the Spitzer images?



6.9    Correlation of X-ray and 2MASS sources
The table 2mass-for-x.tbl is the result of an automatic cross-correlation of the X-ray source list
with the 2MASS database. It lists the 2MASS photometry for those 28 X-ray sources, for which
a 2MASS counterpart was found within 2”. The columns jm , hm , and km contain the JHK
magnitudes.

Action 13: Put these mangitudes into the file 2mass-x.dat that contains an array for each of
the three magnitudes.



6.10    Near-infrared color-color diagram
From these data one can now produce a H − K versus J − H color-color-diagram for the X-ray
selected stars. This can be done by using a simple IDL script. Type idl and then

       @ccd-praktikum.plot

The resulting plot is saved into a postscript file that can be inspected by entering

       $gv ccd.ps &


Action 14: How many of the X-ray sources show infrared excesses? How many sources are within
the reddening band?



6.11    Correlation of 2 MASS and Spitzer sources
The table gaia-input.tbl contains 2MASS JHK magnitudes for 66 sources identified in the Spitzer
images. We will now determine the fluxes of these objects in the four Spitzer filters with the help
of aperture photometry.
For this task the “Graphical Astronomy and Image Analysis Tool” (GAIA) will be used (Fig. 8).
Start the program by typing gaia on the shell. A window will appear and one of the four Spitzer
images can be loaded: spitzer-irac1.sdf (3.6 µm), spitzer-irac2.sdf (4.5 µm), spitzer-irac3.sdf
(5.8 µm), or spitzer-irac4.sdf (8.0 µm). Note the special extension of the filenames. Afterwards,
   1
    Please check whether the file contains numbers in scientific notation, i.e. xey . These numbers have to be
substituted manually. Otherwise the file will not fully be loaded.


                                                    15
                                       Figure 8: Main window of GAIA.



                                                the scaling can be adjusted with the help of the menu
                                                View → Cut Levels. To overlay the Spitzer sources for
                                                which J-, H-, and K-band fluxes are already known the
                                                catalogue can be loaded with Data-Servers → Local Cat-
                                                alogs → Load from file .... The sources are then marked
                                                by blue crosses and their magnitudes and coordinates are
                                                displayed in the catalogue window2 .
                                    For the aperture photometry choose Image-Analysis →
                                    Aperture photometry → Results in magnitudes .... A win-
                                    dow with three tabs pops up (Fig. 9). In the first tab the
                                    aperture is chosen. This is done by clicking on the button
                                    Define object aperture and dragging afterwards a circle
                                    around the star. However, the fine-tuning of the aperture
                                    should be done not with the mouse but again in the tab by
                                    adjusting the sliders while the aperture is selected. With
                                    the sliders is also possible to change the sky annulus for
                                    the background determination. Note, the values for the
                                    sky annulus are factors by which the ‘object aperture’ is
                                    multiplied. Another useful function is to copy the chosen
                                    aperture with Copy aperture and to drag the copy with
                                    the mouse to another source. To calculate the flux within
                                    the selected aperture press the Calculate results button.
                                    The results of all apertures are listed in the tab Results. If
                                    a aperture is not well chosen it can be deleted by selecting
Figure 9: GAIA aperture photometry.
                                    it and clicking with the right mouse button to open the

  2
      If the blue crosses don’t appear, please use the menu Options → Set Plot Symbols ... in the catalogue window.


                                                        16
context menu with the function Delete Selected Items. For an investigation of the PSF the tools
in Image-Analysis can be used.

Action 15: For a first training choose one of the moderately bright stars. Check what happens
when the size of the aperture is changed. What is a reasonable size of the aperture and the sky
annulus? Is it possible to get a reasonable aperture photometry for the brighter objects?

Since the Spitzer images provide already surface brightness units, the second tab can be ignored.
Only the photometric zeropoints have to be provided in the field on top of the tabs. A photometric
zeropoint defines the magnitude of an object that is measured with one count when an exposure
time of 1 s is chosen. For the images used here the channels of IRAC have the zeropoints 22.3 mag
(3.6 µm), 21.6 mag (4.8 µm), 19.5 mag (5.8 µm), and 20.0 mag (8.0 µm).

Action 16: Derive for as many as possible objects the magnitudes in the four IRAC channels.
Note the catalogue numbers of the objects to allow a later comparison.



6.12    Infrared Classification
The derived magintudes can now be used to discriminate the infrared classification of the young
stars. This infrared classification scheme is based on a the spectral index a, which is defined as
follows:

                                              d log (λFλ )
                                       a :=                .                                 (4)
                                                d log λ
Objects with a > 0.0 are in class I, objects with 0 > a > −1.6 in class II, and objects with
a < −1.6 in class III. To determine the spectral index from the measured magnitudes one has
to translate the magnitudes into fluxes. This is done by using the magnitude zero-points for the
individual bands listed in the following table:

                                   Band          λ     flux density
                                               [µm]       [Jy]
                               J (2MASS)        1.2        1590
                               H (2MASS)        1.6        1020
                               K (2MASS)        2.2         667
                                 IRAC 1         3.6        280.9
                                 IRAC 2         4.5        179.7
                                 IRAC 3         5.8        115.0
                                 IRAC 4         8.0        64.13

The listed fluxes correspond to zero magnitude in the given band. Magnitude and flux are related
by the usual relation

                                       F/F0 = 10−m/2.5 .                                     (5)

The Flux Density Fλ gives the flux of energy per time interval dt, in the wavelength interval
[ λ , λ + dλ ], through an area dσ:

                                                17
                                                  dE
                                      Fλ :=             .                                  (6)
                                               dt dσ dλ
Fλ has the unit of erg/sec/cm2 /µm. In an analog way, the flux density can be defined as a
function of frequency ν rather than wavelength λ:

                                                  dE
                                       Fν :=            .                                  (7)
                                               dt dσ dν
Fν has the unit of erg/sec/cm2 /Hz. In astronomy, the flux density is often measured in the unit
Jansky, which is defined as

                                1 Jy = 10−23 erg/sec/cm2 /Hz .                             (8)
It can be easily shown that Fλ and Fν are related by Fλ d λ = −Fν d ν. With c = νλ it follows
                c
that → Fλ = λ2 Fν

Action 17: What are the infrared classes of the objects?




                                               18

				
DOCUMENT INFO
Shared By:
Categories:
Stats:
views:13
posted:4/18/2011
language:German
pages:20