Friday, April 29, 2011

Milky Way: a Distance to the Galactic Center - 2

Why distance to the galactic center is so important?

The distance from Sun and the center of Milky Way is used as a reference stick for many other extragalactic distance calculations, making its accurate determination a matter of extreme importance.
The only direct method to determine distances to cosmic objects outside the Solar System is trigonometrical parallax. Ground-based telescopes allow to measure parallaxes up to ~0.01-arcsec, which allowed the distance estimates up to 100 pc. We can observe less than 1000 stars at these distances. The Hipparcos satellite measures parallaxes  up to ~0.001 arcsec, which provides good distances out to 1000 pc for about 100,000 stars. After 1000 pc we should employ indirect methods for distance estimates, such as spectroscopic parallaxes and properties of periodic variable stars.
No single method can provide accurate distances on all cosmic scales. Instead, we have to rely on a multi-step multi-method approach carefully choosing each method and calibrating at each step. This makes the Cosmic Distance Scale look like a ladder with a series of steps going from near to far. We should
Calibrate parallaxes based on the orbit of the Earth (the Astronomical Unit);
Calibrate H-R diagram methods based on distances to the stars with measured parallaxes;
Calibrate distances to Cepheid and RR Lyrae stars using H-R diagrams;
Calibrate extragalactic distances based on the known distance to galactic center.
So one must calibrate, calibrate and calibrate.
Because of the above reason, astronomers have tried to accurately measure the distance to the Galactic Center since it discovery in the early 20th century. Before that people still believed that our Solar System is the center of the Milky Way.
While the first estimates provided by Harlow Shapley and Jan Oort were despondently incorrect, recent technological advancements have enabled astronomers to estimate the distance to the galactic center with increasing accuracy.


References:


Carretta and Gratton 2000, Distances, Ages, and Epoch of Formation of Globular Clusters, The Astrophysical Journal, 533:215-235

Carretta, Gratton, Clementini, 2000, Mon. Not. R. Astron. Soc. 316, 721±728 (2000)



Popowski and Gould, 1998, "Mathematics of Statistical Parallax and the Local Distance Scale". arXiv, Ohio State University. Retrieved 2008-10-20.

Percival, Salaris and Kilkenny, 2003, The open cluster distance scale, DOI: 10.1051/0004-6361:20030092



Percival, S., Salaris, M., & Kilkenny, D. (2003). Why distance to the galactic center is so important? Astronomy and Astrophysics, 400 (2), 541-552 DOI: 10.1051/0004-6361:20030092

Wednesday, April 27, 2011

Milky Way: Distance to the Galactic Centre



A reprocessed cropped portion of the 2MASS mosaic of the Milky Way (Cutri et al. 2003). The Galactic bulge exhibits a peanut-like morphology.
The Galactic Center cannot be studied at visible, ultraviolet or soft X-ray wavelengths, because of the interstellar dust that hides it from observation. The available information comes from observations at radio, infrared, sub- millimeter and hard X-rays.


The main problem in estimating the distance to the Galactic Center is a proper calculation of extinction



Extinction is the dimming of light from stars and other distant objects, due the combined effects of interstellar absorption and scattering of light by dust particles. Interstellar extinction increases at shorter wavelengths, resulting in interstellar reddening. Extinction is minor in longer wavelengths - radio and infrared, which makes them more suitable for observing at large distances in the galactic.

Harlow Shapley first established coordinates of the Galactic Center in 1918. He derived distances for many globular clusters (GC), and found that the distribution of GCs was centered at about 15 kpc away from the Sun in the direction of the constellation Sagittarius. Shapley derived his cluster distances based on the brightnesses of individual stars in a cluster when possible, and for those clusters where individual stars could not be resolved, on the size and brightness of each cluster as a whole.


Because many of the GCs, which Shapley studied, are out of the dusty Galaxy plane, the distances that he found were not too severely affected by extinction.


The Shapley’s main argument was that such massive objects as GCs are most likely to be centered on the galactic center. However Shapley's conclusions remained controversial at the beginning, they were eventually accepted by majority of astronomers, and his technique is still considered one of the primary means of determining the distance to the center of the Galaxy.
Picture credit:
http://www.phys.boun.edu.tr/~semiz/universe/far/13.html
Similar studies in the 1970s and 1980s with much better data and absorption corrections yielded half shorter distances - 8 instead of 15 kpc.


The exact distance from the Earth to the Galactic Center is still uncertain. The latest estimates based on both - geometric-based methods and standard candles produce distances of 7.6–8.7 kpc with more than 1Kpc uncertainty.






Eisenhauer, F. et al. (2005) used geometrical-based method combined with near IR imaging spectroscopy (with astrometric accuracy of 75 mas) to observe the central 30 light-days close to the Galactic Center. They determined radial velocities for 9 of 10 stars in the central 0.4”, and for 13 of 17 stars out to 0.7”, limiting stars magnitudes to K~16. They combined the calculated radial velocities with astrometrical data, and then used a global fit technique to derive new improved three-dimensional stellar orbits for 6 S stars in the central 0.5” region. This result in the updated estimate for the distance to the Galactic Center Ro= 7,62 +-0,32 kpc.




The instrumentation they used is SINFONI - a near-infrared (1.1 - 2.45 ┬Ám) integral field spectrograph connected to an adaptive optics module, installed on ESO VLT. The instrument operates with 4 gratings (J, H, K, H+K) providing a spectral resolution around 2000, 3000, 4000 in J, H, K, respectively, and 1500 in H+K. For more information about SINFONI, please refer to the following page: http://www.eso.org/sci/facilities/paranal/instruments/sinfoni/overview.html

Vanhollebeke, Groenewegen, and Girardi (2009) employed the different approach. They used the star population synthesis code called TRILEGAL (TRIdimensional modeL of thE GALaxy, Girardi et al. 2005) to compute colour-magnitude diagrams (CMD) towards the galactic bulge (GB) and Galactic Center. They simulated the photometric properties of stars located towards a given direction and limited simulations to given magnitudes. The simulations were run for several star formation rates and metallicity distributions. Extinction was calculated for each object separately based on its visual extinction value and the distance modulus of the object. Based on their simulations, the distance to the Galactic Centre was determined as R0 = 8.7+-0.57 - 0.43 kpc.

Majaess (2010) used sample RR Lyrae variables from the OGLE survey of Galactic bulge fields to estimate R0 using the standard candles method. Majaess (2010) paid a special attention to the effects that can bias the accurate measurements of R0. These include a) an ambiguous extinction, which in turn imposes a preferential sampling of stars toward the near side of the GB, resulting in a smaller mean value of R0, and b) an uncertainty in characterizing how a mean distance to the group of variable stars relates to R0. The result is R0=8.1+-0.6 kpc.



References:
http://www.phys.boun.edu.tr/~semiz/universe/far/13.html
Vanhollebeke E., Groenewegen M. A. T., Girardi L.. "Stellar populations in the Galactic bulge. Modelling the Galactic bulge with TRILEGAL". A&A 498: 2009. Bibcode 2009A&A...498...95V.
Cutri R.M., et al. 2003, The IRSA 2MASS All-Sky Point Source Catalog of Point Sources, NASA/IPAC, Infrared Science Archive.

Monday, April 18, 2011

Celestial events in April 2011

I made this list of interesting celestial events using the information from the NASA web site and also from the Goddard Astronomy Club mailings. I would like to say thank you to people who are doing such a great job by gathering this information.

So here it is:
On Monday, April 18, evening, the International Space Station (ISS) will fly high above the National Capital area and will be visible with naked eyes (if weather permits). It is going to be the brightest object in the sky, except for the Moon, which will be extremely low in the east-southeast.

According to the PRESS RELEASE from National Capital Astronomers:

"ISS will rise in the West about 9:16 pm EDT, moving up and to the right,
into the heart of the bright stars of the winter sky. About 2 minutes later, she will be flying about 6 degrees right of the bright star Betelgeuse, being about 27 degrees altitude over azimuth 263 degrees. About 91 seconds later, ISS will culminate fairly high in the northwest at about 49 degrees over 326.
About 27 seconds later, she will be due North, about 4 degrees above
the North Star, Polaris. About 77 seconds later, ISS will disappear into the shadow of the Earth in the northeast, being about 20 degrees above 35 degrees."


April 18 - a full Moon. The Moon will be directly opposite the Earth from the Sun and will be fully illuminated as seen from Earth. This type of the full Moon was known by early Native American tribes as the Full Pink Moon . This year, it is also known as the Paschal Full Moon because it is the first full moon of the spring season.


April 21, 22 through 25 - Lyrids Meteor Shower from the constellation Lyra. The Lyrids are usually producing about 20 meteors per hour at their peak. However, this year, the gibbous moon will hide most of the fainter meteors in its glare. Look for meteors radiating from the constellation of Lyra after midnight, and be sure to find a dark viewing location far from city lights.

Monday, April 11, 2011

Measuring stellar distances for stars more than 1000 pc away

This post was inspired by my colleague SAO student, who asked on how we can measure stellar distances for stars which are so far away that their parallaxes are not measurable yet.
For stars more than 1000 pc away parallaxes are not measurable yet, so the only way to estimate distances is using photometry. The connection between star brightness and its distance is known as the inverse-square-law (Equation 1.).
B=(L/2Pid2)
dL=(L/4PiB)1/2
Where, B is the star’s apparent brightness, L is its luminosity (W m-2),
d is its distance to an observer.
Equation 1. needs to be changed if one takes into account the expansion of the Universe, but this is irrelevant for all stars in our Local Group.
We can measure the star’s apparent brightness B; then assume the star’s luminosity L; and then solve Equation 1. for the object's luminosity distance dL. The problem is  that we can only measure star’s brightness B and its apparent magnitude m, while the luminosity and absolute magnitude must be derived in some way.
There are two methods for deriving luminosities – one uses spectroscopic parallaxes and another uses standard candles.[1] Both methods use distant-independent properties of stars, which make them good techniques for distance measurements.
A distance-independent property is the property of star, which doesn’t depend on its distance from an observer. For example, a period for a variable star is a distant-independent property. Star’s spectrum can serve as a distant-independent property. The later, however, is not fully distance-independent and works well only up to 100 000 pc given the current technology level.

Spectroscopic parallaxes

The spectroscopic parallax method uses the observed spectrum of the star as a distance-independent property to derive its luminosity (Figure 1). It involves the following steps:
1.           Choose a star of interest;
2.           Plot a calibrated Hertzsprung–Russell (H-R) diagram for nearby stars with known parallax distances;
3.           Observe spectrum of the star of interest;
4.       The spectral type (OBAFGKML) and luminosity class (I-V) provide the star’s unique location on a calibrated H-R diagram;
5.       Once the star’s position on the H-R diagram is known, we can deduce its absolute magnitude (M).
Figure 1. Spectroscopic parallax. Image, courtesy of Prof. Richard Pogge, Ohio State Univ.
As soon as we derived m from measurements and M from the H-R diagram, we can use the distance modulus (Equation 2.) to find the distance to the star - d, in parsecs.
However, the spectroscopic parallax method suffers uncertainties, which range from about 0.7 up to 1.25 absolute magnitudes, which in turn gives a factor of 1.4 to 1.8 variation in the distance (ScienceVaultWeb 2010):
·      The assumption was made that the spectra from distant stars of interest are the same as spectra from nearby stars.
·      Due to difficulties in observing spectra, it works up to 100 000 pc only.
·      Interstellar dust can scatter the different frequencies in different ways, making the identification of spectral class even harder.
·      Matter between the star and the observer would absorb some of the light and make the star's apparent brightness less than it should be.
·      The star’s location on H-R diagram depends on its composition and luminosity class, which is difficult to determine for distant stars due to faint spectra. And there are many stars, which don't belong to the Main Sequence.
Spectroscopic parallaxes, however, work well for star clusters, where one can average out many measurements. Since all of the stars in the cluster are the same distance away from us, all of them will have an equal displacement along the Luminosity axis on H-R diagram. Therefore, the cluster's Main Sequence will appear to be shifted vertically in the H-R diagram from the nearby stars. Now, we can measure how much we have to shift the entire set of nearby stars so that they overlap the Main Sequence of the cluster, and can estimate how far away the cluster is.
The distances to the closest clusters, e.g. Hyades (46.34 pc), Pleiades (135 pc) can be measured directly using the parallax method (Perryman et al. 1998, HipparcosESAWeb). Once nearby open cluster distances are determined, they can be used to estimate the distances to other open clusters, up to 10—15 kpc away. Once the distances to Pleiades is determined, the distance to a Cepheid Variables can be calibrated (Popowski and Gould 1998; Percival, Salaris and Kilkenny, 2003).

This is important: since the only directly measurable distances in astronomy are those made by trigonometric parallax, the results from other techniques should be calibrated using parallax data.

Cepheids and RR Lyrae stars as standard candles

Cepheids and RR Lyrae are variable stars whose brightness varies regularly with a characteristic, periodic pattern. Period of their brightness variations is a distance-independent property and can be used for estimating distances to these stars.
Cepheids are located in the upper part of the instability strip in the H-R diagram, while RR Lyrae in the lower part. Most massive stars enter the instability strip and become variable after they have left the main sequence (Figure 2.)
In 1912 Henrietta Leavitt (1868—1921) published the results of her study of variable stars in the Large and Small Magellanic Clouds. She found that the fainter Cepheids have shorter pulsating periods. Because all Cepheids in a Magellanic Cloud are at the same distance from us, Leavitt concluded that the more luminous Cepheids pulsated more slowly.
In 1950's astronomers found that there are actually two types of Cepheids:
1.    Type I or classical Cepheids are from young high-metallicity stars and are about 4 times more luminous than Type II;
2.   Type II or W Virginis Cepheids.
Type I Cepheids are young high-metallicity stars 4 times more luminous than Type II Cepheids. Application of the classical Cepheid P-L relation to W Virginis Cepheids may lead and did lead to a large overestimation of the distances.

Figure 2. Cepheids and RR Lyrae on H-R diagram – the instability strip. Cepheids and RR Lyrae are variable stars whose brightness varies regularly with a characteristic, periodic pattern. Period of their brightness variations is a distance-independent property and can be used for estimating distances to these stars. Cepheids are located in the upper part of the instability strip in the H-R diagram, while RR Lyrae in the lower part. Most massive stars enter the instability strip and become variable after they have left the main sequence. Figure credit: ScienceVaultWeb.

How this method works:

1.    Photometric observations provide the apparent magnitude values for the variable star.
2.   Plotting apparent magnitude values from observations at different times against phase (or time) creates a light curve.
3.   From the light curve and the photometric data the average apparent magnitude, m, of the star and its period in days can be obtained.
4.   The mean absolute magnitude, M, can be obtained by interpolating on the period-luminosity plot.
5.    Once apparent magnitude, m, and absolute magnitude, M are known we can simply substitute in to the distance-modulus to obtain the distance to the star.
The question arises “How precise we can measure the period-luminosity (P-L) relation for a given star?”

Baade-Wesselink Method

The classical method that derives the distance of a pulsating star by comparing its linear radius variation, estimated from the radial velocity curve, with its angular radius variation, which can be estimated from the light curve. The method is named after Walter Baade and the Dutch astronomer Adriaan Jan Wesselink (1909–1995).
The recent advances in interferometry and observational techniques allowed the direct detection of pulsations in nearby Cepheids and RR Lyrae, providing an independent distance measurement of pulsating stars (Cox 1980, Marengo et al. 2004).

Issues with using distance measurement techniques for Cepheids and RR Lyrae

Studies show that in estimating distances using P-L relation an individual Cepheid could deviate up to ± 0.6 mag in B. Such an error if applied to an individual star would end up into an error of about 30% in distance (CaltechCepheidsWeb 2010). Therefore, large samples needed to decrease the error.
The error on the apparent modulus decreases inversely with the square root of the number of samples, so decreasing an error from 30% to 10% is possible with a sample containing a dozen Cepheids.
The other issues include the systematic effects of reddening and the systematic effects of metallicity,.
Interstellar dust absorbs light, particularly at blue wavelengths. This dust absorption can lead to erroneous luminosity-color determinations, so a Cepheid from an external galaxy will appear both –fainter and more distant and redder and cooler – than it actually is. Systematic errors due reddening, if not corrected, will affect the distance scale.
The role of metallicity in the evolution of individual Cepheids and how it affects P-L relation and classic B-W method has been a matter of debate for several decades. Gieren et al. (1998, 2005) found a significantly different slope between the Galactic and LMC samples of Cepheids based on ISB analysis of Galactic and LMC Cepheids.
Trigonometric parallaxes for RR Lyrae were determined by HIPPARCOS and HST. However, only data for RR Lyr and 2 others were considered to be accurate enough (Benedict et al., 2002, Carretta and Gratton 2000). This makes calibration for P-L and B-W methods difficult.

References:

BENEDICT et al., 2002, ASTROMETRY WITH THE HUBBLE SPACE TELESCOPE: A PARALLAX OF THE FUNDAMENTAL DISTANCE CALIBRATOR RR LYRAE, THE ASTRONOMICAL JOURNAL, 123:473-484
Carretta and Gratton 2000, Distances, Ages, and Epoch of Formation of Globular Clusters, The Astrophysical Journal, 533:215-235
Carretta, Gratton, Clementini, 2000, Mon. Not. R. Astron. Soc. 316, 721±728 (2000)
Cox, J.P. 1980, in Theory of Stellar Pulsation, (Princeton University Press, Princeton)
Gieren, W.P., Fouque, P., & Gomez, M.; 1998, AJ, 496, 17
Gieren, W., Storm, J., Barnes, T.G., et al.; 2005, ApJ, 627, 224
Marengo M., Karovska M., Sasselov D., 2004, AN ERROR ANALYSIS OF THE GEOMETRIC BAADE-WESSELINK METHOD, The Astrophysical Journal, 603:285–291
Perryman et al., 1998, The Hyades: distance, structure, dynamics, and age, arXiv:astro-ph/9707253
Perryman et al., 1999, "The HIPPARCOS Catalogue". Astronomy and Astrophysics 323: L49–L52. Retrieved 2008-10-18.
Popowski and Gould, 1998, "Mathematics of Statistical Parallax and the Local Distance Scale". arXiv, Ohio State University. Retrieved 2008-10-20.
ScienceVaultWeb- http://sciencevault.net/ibphysics/astrophysics/stellardistances.htm


[1] The term spectroscopic parallax is a misnomer, as it actually has nothing to do with trigonometric parallax. It is, however, a legitimate way to find distances to stars.

Carretta, E., Gratton, R., Clementini, G., & Fusi Pecci, F. (2000). Distances, Ages, and Epoch of Formation of Globular Clusters The Astrophysical Journal, 533 (1), 215-235 DOI: 10.1086/308629