Astrophysical validation of Gaia parallaxes Fredrik Windmark Lund Observatory Lund University 2010-EXA39 Degree project of 60 higher education credits (for a degree of Master) June 2010 Lund Observatory Box 43 SE-221 00 Lund Sweden Acknowledgements I want to thank my supervisor Lennart Lindegren for his help and for sharing his great knowledge and experience. I also want to thank my co-supervisor David Hobbs for his help with the project in general, and the Java programming in particular. Working with this Masters project has been an incredibly fun and rewarding time. Big thanks also go to Berry Holl for his help with simulating the Gaia parallax measurements. I have also had countless helpful discussions with my office mate To- bias Albertsson, to whom I owe a lot. Worth mentioning are also my fellow Master students; Nils H˚akansson, Hannes Jensen and Carina Lagerholm, who have been re- ally helpful and have had to put up with all my rambling during these two years. My girlfriend Maria Ewerl¨ofhas also been incredibly patient with me, and her support has meant a lot. Abstract The Gaia satellite, to be launched in August 2012, will measure highly accurate absolute parallaxes of hundreds of millions of stars. This is done by comparing parallactic displacement of stars in different parts of the sky. The accuracy of this method highly depends on the stability of the so-called basic angle between the two fields of view of the Gaia instrument, and periodic variations could lead to a global zero-point error in the measured parallaxes. Small variations of the basic angle are closely monitored by on-board instruments, but independent verification methods are also needed. In this project, we use Galactic Cepheid variables as standard candles to compare with the observed parallaxes at a wide range of distances. If there is a parallax zero-point error, the observed parallaxes will not be consistent with a single Period- Luminosity relation. A model is formulated where the complete Galactic Cepheid population is generated and observed in a simulated Gaia mission. Using the ob- served Cepheids, we then make simultaneous fits to the P-L relation and the parallax zero-point in order to determine whether using Cepheids is a viable zero-point veri- fication method. Our simulations show that Gaia will observe about 9000 Galactic Cepheids, fifteen times the currently known number. Gaia will alone result in large improvements in the accuracy with which the Galactic P-L relation can be determined. Both con- stants in the relation can be determined with an accuracy of σa;b < 0:05. We show that using Galactic Cepheids, the parallax zero-point can be determined with an accuracy of σc = 0:3 µas, with the largest error contribution coming from the un- certainty with which we can determine the extinction. This is very good, but not enough for the most demanding tasks of Gaia. We conclude that the global verifi- cation of the parallax zero-point ultimately will depend on a combination of many different methods. Sammanfattning I augusti 2012 kommer Gaia-satelliten, en rymdsond utvecklad av ESA, att skju- tas upp f¨oratt under fem ˚arobservera hundratals miljoner stj¨arnor.Gaia kommer bland annat att m¨ataparallaxen, eller avst˚andet,till alla dessa stj¨arnormed en nog- grannhet som ¨artusen g˚angerb¨attre¨andess f¨oreg˚angareHipparcos. Antalet stj¨arnor kombinerat med den stora noggrannheten inneb¨aratt Gaia kommer att utf¨oraden st¨orstaoch mest noggranna kartl¨aggningenav Vintergatan n˚agonsin.Detta kommer garanterat att leda till ett otal vetenskapliga uppt¨ackter, men f¨oratt med s¨akerhet kunna anv¨andadatan ¨ardet viktigt att p˚an˚agots¨attverifiera att m¨atningarna¨ar sanna. I det h¨ararbetet unders¨oker vi om denna verifiering skulle kunna ske med hj¨alp av s˚akallade cepheider i Vintergatan. Cepheider ¨arj¨attestj¨arnorsom varierar i stor- lek och ljusstyrka med en period som beror p˚ahur stor massa de har. Detta inneb¨ar att man genom att m¨atahur l˚angen cepheids period ¨arkan best¨ammadess avst˚and fr˚anoss utan att beh¨ova m¨ataparallaxen. Denna egenskap har gjort cepheiderna till en av de viktigaste metoderna f¨oratt kunna m¨ataavst˚andutanf¨orv˚aregen galax, och en stor del av v˚aruppfattning om universum beror idag p˚adem. Det borde ¨aven vara m¨ojligtatt anv¨andadem f¨oratt bekr¨aftaGaias parallaxm¨atningar. F¨oratt kunna avg¨orahur bra cepheider ¨arf¨ordetta ¨andam˚alm˚astevi veta hur m˚angaGaia kommer att observera i Vintergatan. Eftersom vi bara k¨annertill de cepheider som ligger allra n¨armastsolen, och Gaia kommer att kunna se ¨aven dem i andra ¨anden av galaxen, s˚am˚astevi simulera hur cepheidernas f¨ordelningi Vin- tergatan kan t¨ankas se ut. Sedan, eftersom Gaia fortfarande inte blivit uppskjuten, m˚astevi ¨aven simulera Gaias observationer. Med v˚arasimulationer visar vi att Gaia kommer att observera fler ¨an9000 cepheider i Vintergatan, vilket kan j¨amf¨orasmed de 600 man k¨annertill idag. Cepheid-metoden kommer att kunna bekr¨aftaGaias parallaxm¨atningarmed en noggrannhet p˚aungef¨ar 0.3 mikrob˚agsekunder.Detta ¨armycket bra, men inte tillr¨ackligt f¨orde allra mest kr¨avande uppgifter som Gaia ¨arkapabel till att utf¨ora.Verifieringen av Gaias par- allaxer kommer troligen inte att kunna ske med hj¨alpav en enda metod, utan m˚aste nog snarare ske med ett antal olika, d¨arVintergatans cepheider kommer att spela en viktig roll. Contents 1 Introduction 1 2 The Gaia Mission 2 2.1 The Gaia basic angle . .4 3 Methods of parallax validation 6 3.1 Quasars . .6 3.2 Cepheids . .7 4 Cepheid properties 8 4.1 General properties . .8 4.2 The Cepheid P-L relation . .9 4.3 Cepheid catalogue data . 10 5 Galaxy modelling 15 5.1 Framework for Galaxy modelling . 15 5.2 Cepheid distribution . 16 5.2.1 Radial distribution . 17 5.2.2 Vertical distribution . 20 5.2.3 Total number of Galactic Cepheids . 22 5.2.4 Period distribution . 24 5.2.5 Magnitude distribution . 26 5.3 Extinction and apparent magnitudes . 28 6 The Gaia model 31 7 Statistical analysis 32 7.1 Parameter fitting . 33 7.2 Measurement errors . 36 8 Results 37 8.1 The simulated galaxies . 39 8.2 Results of the parameter fitting . 45 8.2.1 Typical experiments . 47 8.2.2 Other experiments . 50 8.2.3 Limiting the sample . 50 9 Discussion and conclusions 55 A Table of notations 59 B The CepheidObsModel program 61 B.1 The Galaxy . 61 B.2 The Observer . 63 B.3 Gaia . 63 B.4 Statistics . 65 C Experiment tables and plots 65 1 INTRODUCTION 1 Introduction The Gaia satellite, due for launch in August 2012, is the successor to the successful Hipparcos mission, an ESA space astrometry mission that was active in the early 90's. The Hipparcos data had a very large impact on the world of astronomy, with its primary catalogue containing approximately 120 000 stars covering the whole sky with a median parallax accuracy of 1.1 milliarcseconds (mas) (Perryman et al. 1997). The advantage of working with large, homogeneously determined data sets is clear. Even today, the Hipparcos mission remains the largest astrometric all-sky survey. This will change with the advent of Gaia, which will result in a catalogue containing roughly a billion objects with parallax accuracies reaching below 10 microarcseconds (µas) (Lindegren & Perryman 1996; Lindegren 2010). With a catalogue ten thou- sand times larger and a hundred times more accurate than what we currently have, along with simultaneous astrometric, photometric and spectroscopic observations, it is safe to say that Gaia will result in a revolution in the understanding of stellar and Galactic dynamics, formation and evolution (Perryman et al. 2001). Achieving the desired accuracy requires an exceedingly stable optical instrument for the Gaia satellite, as even extremely small variations in the basic angle could lead to an undesirable global shift in the parallax zero-point. To be able to deter- mine the absolute parallax of an object, Gaia simultaneously observes stars in two regions on the sky that are separated by a large basic angle. The two fields of view cross the same part of the sky with a separation in time of the order of a few hours, and it is the relation between the parallaxes measured in the two fields that lies behind Gaia's ability to do global astrometry and to determine absolute parallaxes. The stability of the basic angle is therefore of great importance to avoid introducing errors in the parallax measurements. As the satellite rotates, however, different parts will be exposed to solar heating. This will inevitably lead to basic angle variations on the scale of hours, creating apparent image shifts that may be indistinguishable from a global offset of all parallaxes (Lindegren 2004). An on-board laser interfer- ometer is therefore used to measure these variations so that they can be included in the instrument calibration model. However, it is still desirable to verify the paral- lax accuracy, and in particular the parallax zero-point, by independent astrometric means. One example where the knowledge of the Gaia parallax bias is of great importance is for the use of distance determination to the Large Magellanic Cloud (LMC). This is very important to the extragalactic distance scale, and its distance of around 50 kpc (or 20 µas) is today known with an uncertainty of 5%. It is believed that Gaia will 7 observe 10 stars in the LMC with a meanp standard error of about 200 µas, which would result in a mean parallax of 200= 107 ≈ 0:06 µas, corresponding to a relative precision of 0.3%.