Tracing the Perseus Spiral Arm in the Anticenter Direction

Tracing the Perseus spiral arm in the anticenter direction

Maria Monguió i Montells

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Tracing the Perseus spiral arm in the anticenter direction

Mem`oria presentada per Maria Mongui´o i Montells

per optar al grau de Doctor per la Universitat de Barcelona

Barcelona, Setembre de 2013 2 . 3 ProgramadedoctoratenF´ısica

Mem`oria presentada per Maria Mongui´o i Montells

per optar al grau de Doctor per la Universitat de Barcelona

Directors de la tesi:

Dra. Francesca Figueras Dr. Preben Grosbøl

Tutora de la tesi:

Dra. Francesca Figueras 4

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res

“La gent té estrelles que no són iguals. Per uns, els que viatgen, les estrelles són guies. Per altres només són llumets. Per altres, que són savis, són problemes. Peròtotes aquestes estrelles callen. Tu tindràs estrelles com no en téningú.” El petit pr´ıncep, Antoine de Saint-Exupéry.

“All men have the stars, but they are not the same things for diﬀerent people. For some, who are travelers, the stars are guides. For others they are no more than little lights in the sky. For others, who are scholars, they are problems. But all these stars are silent. You -you alone- will have the stars as no one else has them.” The little prince, Antoine de Saint-Exup´ery. 6

. Acknowledgments / Agra¨ıments

I would like to thank Dra. Francesca Figueras Siñol and Dr. Preben Grosbøl, for giving me the oportunity to develop this thesis. For everything they taught me, all the things we’ve learned together, all their support, and all the moments in the offices in Barcelona, in Garching, and also in some telescope control room. Cesca, merci per les hores, les correccions, les bromes, la paciència, els cafès, i tantes i tantes coses... Mil gràcies! Preben, thank you for not only telling and showing, but also involving me. Tak! També vull agrair el suport de l’equip Gaia, encap¸calat pel Dr. Jordi Torra, la Dra. Carme Jordi i el Dr. Xavi Luri. A la Lola (Dra. Balaguer-Núñez), per tot el suport cient´ıfic, log´ıstic i moral; al Dani per totes les re-instal·lacions; aix´ı com a la resta de cient´ıfics i enginyers del grup. Gràcies a l’IEEC, a l’ICC i al Departament d’Astronomia i Meteorologia de la Universitat de Barcelona, aix´ı com a tots els seus membres. I especialment al JR, al Jordi, la Montse, la Rosa i al Gaby: espero haver-vos emprenyat una mica, però no massa. Thanks to the European Southern Observatory, for all the nice stays I have done both, in Garching and in Santiago de Chile, y especialmente al Dr. Giovanni Carraro. A la Teresa, la Mercè, la Maria, el Santi, la Hoda i la Laia; gràcies per compartir ciència, caipirinyes, simulacions, viatges, programes fortran, en python, i tot el que s’ha necessitat. A la colla de doctorants del DAM, per haver pogut compartir penes i alegries durant tots aquests anys. A la Laura, per compartir cam´ı(iperquè no importa les raons que tu tinguis, ella sempre guanya). A la Rosa i la Neus per les confidències (i la carros!). Al Pere, al Jordi, a l’Héctor, al Javi, al Pau, a la Carme, a la Gemma, al Sinu, al V´ıctor, al Josep Maria, a l’Alvaro, al Xavi, al Benito, (i als que em deixo!) perquè segons diu l’anunci, he passat amb vosaltres totes les diminutes vacances (o els petits caps de setmana) de cada dia, durant elsultims ´ cinc anys. Als amics de fora de l’astronomia. Als de Quanca per les nits estrellades als Pirineus. Als de futbol per permetre’m desconnectar. Per confondre’m amb una astròloga, preguntar-me pels extraterrestres, els salts del Baumgartner i els forats negres. Per tractar-me de friqui quan apuntant amunt asseguro que aquell punt és Saturn, i alhora flipar amb el làser i el telescopi. Isobretotalamevafam´ılia. Als meus pares, per ser-hi sempre. Al Pere, per tot el que n’aprenc i tot el que em fa enrabiar. A lesavies ` perquèmelesestimomolt´ıssim. Als cosinets figueros d’aqu´ı i de per tot arreu, per les cerveses, els partits del Bar¸ca, les esquiades, i els minifigos, que són tots per menjar-te’ls!

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This work was supported by the FPI grant (BES-2008-002471 through ESP2006-13855-C02- 01 project) of Miniterio de Ciencia y Educaci´on and the Spanish Ministry of Economy MINECO - FEDER through grants AYA2009-14648-C02-01, AYA2010-12176-E, AYA2012-39551-C02-01 and CONSOLIDER CSD2007-00050. The results of this work are based on observations made with the ING telescopes operated on the island of La Palma at the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astroﬁsica de Canarias, and with the 1.5m telescope of the German Spanish Astronomical Center, Calar Alto, operated jointly by the Max Planck Institut fur Astronomie and the Instituto de Astrof´ısica de Andaluc´ıa. This research has made use of Aladin, Vizier and Simbad, developed by CDS, Strasbourg, France; TOPCAT & STILTS: Starlink Table/VOTable Processing Software developed by M.B. Taylor, and the WEBDA database, operated at the Department of Theoretical Physics and Astrophysics of the Masaryk University. During this thesis several visits to the Europen Southern Observatory have been done, both in Garching (Germany) and Santiago (Chile). We also want to thank Dr. Maria Czekaj and Dr. Annie Robin for providing us simulations of the new version of the Besan¸con Galaxy Model. Resum

La nostra Galàxia és un sistema d’unes 1011 estrelles, gas interestel·lar i petites quantitats de pols, on també hi podem trobar camps magnètics a través dels quals hi viatgen part´ıcules de rajos còsmics. Tot i això, són les forces gravitacionals les que governen l’estructura i la cinemàtica del sistema. Superposat a tota aquesta distribució hi podem trobar l’estructura espiral, que tot i estar distribu¨ıdaatravés de tota la Galàxia, també consta de petites agrupacions i irregularitats. Han passat més de 150 anys des que William Parsons (1800-1867) va detectar, l’any 1845, l’estructura espiral de M51. No obstant, no va ser fins l’any 1952 que W.W. Morgan va trobar, per primera vegada, evidències de l’estructura espiral a la Via Làctia, a través d’observacions de regions d’hidrogen ionitzat, tot obtenint les seves distàncies a partir de paralaxis espec- troscòpiques. Avui en dia, i després de molts anys d’investigació, encara no disposem d’una teoria completa sobre la forma i l’origen dels patrons espirals de la Via Làctia. I tot i ser conscients que són un factor important per explicar l’evolució dels discos galàctics, la manca d’evidències observacionals sobre els bra¸cos espirals de la nostra Galàxia és evident. Moltes preguntes clau encara no tenen resposta, com ara: quin és el mecanisme de formacióievolució de l’estructura espiral en discs estel·lars? Es tracta d’estructures transitòries o són estructures de llarga durada? Quins són els seus components bàsics; estrelles o gas? El treball realitzat durant aquesta tesi pretén ajudar a resoldre algun d’aquests interrogants. El principal objectiu és tra¸car el bra¸c espiral de Perseu en la direcció de l’anticentre Galàctic. La feina desenvolupada es pot separar en tres apartats. En primer lloc, un mostreig amb fotometria Strömgren en la direcció de l’anticentre Galàctic, mitjan¸cant el qual hem obtingut un catàleg de 96.980 estrelles, 35.974 d’elles amb informació completa en els sis filtres uvbyHβ, i totes elles en una regió de 16 graus quadrats del cel. En segon lloc, per tal d’obtenir els paràmetres f´ısics per a aquestes estrelles, hem creat un nou mètode a partir de models atmosfèrics i evolutius. Finalment, s’ha utilitzat tota aquesta informació per estudiar la distribució de la densitat estel·lar en la direcció de l’anticentre. Aquestes dades també ens han permès crear un mapa d’extinció tridimensional, a partir del quan hem analitzat la distribuciódepolsaix´ı com la seva relació amb el bra¸cespiraldePerseu.

Nou catàleg de fotometria Strömgren en la direcció de l’anticentre

La Wide Field Camera (WFC) situada a l’Isaac Newton Telescope (INT), ens ha permès utilitzar elsfiltresStrömgren uvbyHβ en un mosaic de CCDs amb un camp de visióde∼ 0, 5◦ ×0, 5◦.Han estat necessàries diverses campanyes observacionals per cobrir els ∼16◦ del mostreig. Aquest consta de dues regions de cel amb diferents caracter´ıstiques. La regióinternaté una magnitud l´ımit més profunda, i cada camp ha esta observat fins a tres vegades amb petits despla¸caments per

9 10 tal de minimitzar els efectes dels p´ıxels defectuosos i dels raigs còsmics. La regióexternaté una magnitud l´ımit més brillant, i cada camp s’ha observat només una vegada. El mostreig compta amb 96.980 estrelles, amb precisióastromètrica entorn a 0,02, i amb fotometria en almenys un dels sis filtres disponibles (u, v, b, y, HβW i HβN ). Però ens calen tots els sis filtres per tal de crear els ´ındexs (V,m1,c1,Hβ), i aix´ı poder-ne calcular els paràmetres f´ısics. Només 35.974 d’aquestes estrelles compleixen aquesta condició, i per tant podran ser utilitzades per a l’estudi. Les precisions en fotometria obtingudes varien amb la magnitud V , i van des d’unes poques centèssimes de magnitud per les estrelles brillants, fins a ∼0.1 magnituds per a alguns ´ındexs i per a estrelles febles. L’àrea observada s’ha centrat lleugerament per sota del pla galàctic per tal de tenir en compte l’alabeig del disc, i cobreix longituds galàctiques entre l ∼177◦ i l ∼183◦, i latituds entre b ∼−2◦ i b ∼ 1.5◦.

Nou m`etode de derivaci´o de parametres f´ısics

Hi ha disponibles a la literatura diverses calibracions per tal d’obtenir els paràmetres f´ısics a partir de fotometria Strömgren. Referències com ara Crawford (1978, 1979), Balona & Shob- brook (1984), Claria Olmedo (1974), Grosbol (1978) o Hilditch et al. (1983) presenten mètodes lleugerament diferents que hem comparat amb dades del catàleg Hipparcos. Els biaixos i les diferències obtingudes han estat utilitzats per tal de triar la millor opció en cada cas i con- struir el mètode de calibracióemp´ırica (EC, per les seves sigles en anglès) que ens proporciona distàncies, magnituds absolutes i absorcions per a les estrelles del nostre catàleg. Atès que el nostre objectiu és utilitzar les estrelles joves, només hem calculat els paràmetres f´ısics de les estrelles de les regions 1-2-3, és a dir, estrelles calentes fins a tipus espectral A9. Aquest mètode necessita una classificacióprèvia de les estrelles en regions, fet que pot comportar discontinu¨ıtats en els resultats. D’altra banda, proposem un nou mètode basat en models (MB, per les seves sigles en anglès) per a calcular els paràmetres f´ısics a partir de la fotometria Strömgren. S’utilitzen tres ´ındexs lliures d’extinció, [m1], [c1],Hβ, per fer correspondre cada estrella amb un dels punts de la xarxa del model atmosfèric, utilitzant també els errors fotomètrics corresponents. S’ha comparat els models disponibles Castelli & Kurucz (2004), Smalley & Dworetsky (1995) i Smalley & Kupka (1997) per tal de trobar la millor xarxa possible. A continuació, hem utilitzat els models evolutius de Bressan et al. (1993) i Bertelli et al. (2008) per a calcular els caracter´ıstiques finals per cada estrella. De nou, s’ha desenvolupat comparacions amb dades d’Hipparcos per tal d’optimitzar les malles per a estrelles fins a temperatures efectives de 7000K. Aix´ıdoncs,elsparàmetres f´ısics proporcionats per estrelles més fredes poden estar esbiaixats ja que no han estat comprovats. Aquest mètode no necessita de classificacióprèvia en regions, evitant discontinu¨ıtats. De totes maneres, encara podem trobar ambigüitats entre les estrelles primerenques i les tardanes, ja que queden situades, en l’espai [m1] − [c1], en una regió on es poden confondre. Les estrelles amb errors grans d’alguna de les dues regions poden quedar situades amb facilitat molt a prop de l’altra regió, portant a errors de classificació. Aquest és un problema dif´ıcil de resoldre, i que està present tant en el mètode EC com al MB. Tot i això, en alguns casos, les dades de 2MASS ens poden ajudar a resoldre aquesta ambigüitat. La comparacióentreelsdosmètodes ens dóna resultats similars, tot i que podem trobar un biaix en les distància d’un 20%, principalment a causa de les diferents calibracions en magnitud absoluta utilitzades. Els paràmetres f´ısics obtinguts també s’han comparat i complementat amb dades de catàlegs externs. El catàleg d’IPHAS ens ha ajudat a identificar i treure de la mostra les estrelles amb 11 l´ınies d’emissió. A més, les dades de 2MASS ens permeten comparar l’absorció en l’infraroig amb els nostres resultats, i aix´ı obtenir un indicador de la qualitat dels nostres resultats, especialment alaregió del diagrama [m1]−[c1] entre les regions primerenca i tardana, on certes estrelles poden estar mal classificades.

La sobredensitat estel·lar i la capa de pols associades al bra¸cdePerseu

Per estudiar la distribució radial de la densitat de les estrelles a la direcció de l’anticentre, hem de seleccionar les estrelles que sónutils ´ per a aquest propòsit. En primer lloc, hem exclòs les estrelles més fredes de 7000K. Aix´ı mateix, les estrelles que siguin classificades com d’emissióa partir de les dades d’IPHAS també seran excloses. A continuació, diferents criteris ens ajudaran a netejar la mostra, tot eliminant aquelles estrelles que tinguin informació dubtosa. D’aquesta manera, utilitzarem diverses mostres de dades, amb informaciómés o menys precisa, i amb més o menys nombre d’estrelles. Obtenim la magnitud l´ımit per totes les mostres per tal de poder calcular la seva completitut en funciódeladistància. Atès que estem estudiant la variació de la densitat d’estrelles a diferents distàncies, hem d’estar completament segurs que tenim mostres completes a una certa distància. Si és aix´ı, la variació de densitat que puguem trobar, serà degudaunicament ´ a causes f´ısiques (radi d’escala, sobredensitat estel·lar, etc.), però no a causa dels biaixos observacionals. Aix´ı doncs, hem calculat l´ımits en la magnitud absoluta per a cadascuna de les mostres per tal de crear mostres completes fins a 3 kpc, ja que esperem trobar el bra¸cdePerseumés proper a aquesta distància. D’altra banda, la saturació d’estrelles molt brillants tambéimposaunl´ımit de completitut per a estrelles properes a 1,2 kpc, i per tant, també estableix un l´ımit per a magnituds absolutes intr´ınsiques més brillants. Per tal de calcular aquests l´ımits màxim i m´ınim en les magnituds absolutes intr´ınseques hem utilitzat la magnitud visual V aix´ı com l’absorció en el visible obtingudes a 1,2 i 3 kpc. Utilitzant les mostres completes entre 1,2 i 3 kpc, i un cop aplicats els talls en magnituds intr´ınseques a cadascuna de les mostres, podem estudiar la distribució de densitats en funcióde la distància. L’estudi de la densitat superficial és la millor opció, ja que pot tenir en compte els efectes de l’al¸cada patródelaGalàxia, l’alabeig del disc present en aquesta direccióolaposició del Sol per sobre del disc Galàctic. S’han obtingut diferents distribucions de densitat superficial per a cada una de les mostres, diferents mides de bin, regions de cel i també utilitzant els dos mètodes disponibles per al càlcul de la distància, EC i MB. També hem ajustat el radi d’escala de la Galàxia per a cadascun d’ells. Les distribucions obtingudes amb el mètode MB mostren en tots els casos una clara sobredensitat al voltant de 1,7 kpc. La sobredensitat obtinguda a partir del mètode EC no és tan clara, encara que tambéés observable en alguns casos. De fet, la presència del bra¸c pot esbiaixar l’ajust del radi d’escala, aix´ı doncs hem repetit els ajustos evitant els punts propers a la regió de la sobredensitat. El rang de valors obtingut per al radi d’escala és [2.0-2.6] kpc. Els ajustos també proporcionen la densitat superficial de la posició del Sol per a cada una de les mostres. En el cas de la mostra d’estrelles amb tipus espectrals B4-A1, s’ha pogut estimar el valor de la densitat superficial a l’entorn solar en 0.022 /pc2. Tot i que els valors esperats per aaquestparàmetre són molt incerts, ja que depenen del rang de magnitud absoluta intr´ınsica utilitzat i també de l’al¸cada patró utilitzada, els valors obtinguts són coherents amb els obtinguts apartirdelanovaversiódelmodeldeGalàxia de Besan¸con. S’han realitzat diversos testos χ2 que ens han permès rebutjar fins a un 5% de significància 12 la hipòtesis que la distribució de densitat obtinguda (al treballar amb el mètode MB i amb les mostres amb més estrelles) és deguda només a una caiguda exponencial. De la mateixa manera, tenint en compte el nombre d’estrelles observades a la regió al voltant del pic, i comparant-lo amb el nombre d’estrelles estimat per la distribució exponencial ajustada, podem calcular una significància per la sobredensitat de 3σ,aix´ı com una amplitud de la sobredensitat al voltant del 10%. Les nostres dades també ens permeten crear un mapa tridimensional de l’absorcióalaregió estudiada. S’ha creat una malla en l, b, r, en cada punt de la qual l’absorció AV es calcula com la mitjana de totes les estrelles disponibles, ponderada per la distància entre el punt i cadascuna de les estrelles. El pes gaussià utilitzat ens permet incloure un paràmetre σ,queserà diferent per cada cada punt, depenent de la densitat d’estrelles al seu voltant. Per als punts propers al Sol, hi haurà una major densitat, és a dir, més estrelles disponibles (tant a causa del radi d’escala com de la magnitud l´ımit) i per tant podrem aconseguir millor resolució. Per als punts en regions de densitat inferior, la σ utilitzada seràmés gran ja que haurem de promitjar per a volums més grans, i la resolució que ens proporcionarà el mapa tridimensional seràmenor.

Mitjan¸cant l’estudi de l’absorció AV en funciódeladistància, i més concretament, la seva variació dAV /dr, trobem un canvi clar de tendència al voltant 1,7 kpc, just on hem detec- tat el bra¸c de Perseu. Aquest fet indica la presència d’una capa de major densitat de medi interestel·lar just abans del bra¸c espiral, i una menor densitat darrere d’aquest. Segons la teoria de Roberts (1972) aquest escenari coincideix amb una capa de pols just abans del bra¸c, indicant que podr´ıem trobar-nos dins del radi de corrotatió. El mapes bidimensionals l, b obtinguts a diferents distàncies ens proporcionen la ubicació de diferents núvols de gas, que coincideixen amb els que hem trobat a la literatura. L’estudi de la variació de l’absorció dAV /dr també pot detectar aquests núvols, proporcionant distàncies molt més precises de les disponibles a la literatura. Abstract

The main purpose of this thesis is to map the radial variation of the stellar density for the young stellar population in the Galactic anticenter direction in order to understand the structure and location of the Perseus spiral arm. A uvbyHβ Strömgren photometric survey covering 16◦ in the anticenter direction was carried out using the Wide Field Camera at the Isaac Newton Telescope. This is the natural photometric system for identifying young stars and obtaining accurate estimates of individual distances and ages. As a result, a main catalog of 35974 stars with all Strömgren indexes has been obtained, together with a extended one with 96980 stars with partial data. The central 8◦ have a limiting magnitude of V ∼17mag, while the outer region reaches V ∼ 15.5mag. These large samples permit us to analyze the stellar surface density variation associated to the Perseus arm and to study the properties of the stellar component and the interstellar extinction in the anticenter direction. To compute the physical parameters for these stars two different approaches have been used, 1) the available pre-Hipparcos empirical calibrations based on cluster data and trigonometric parallaxes, and 2) a new model based method using atmospheric models and evolutionary tracks, optimized for stars up to Teff >7000K. Results for both of them have been compared with Hipparcos data looking for possible biases and trends. The obtained physical parameters allow us to select the intermediate young stars useful for our studies (∼B5-A3). These stars are young enough to still have a small intrinsic velocity dispersion (making them respond stronger to a perturbation), but they are also old enough to have approached a dynamic equilibrium with the spiral perturbation. Through their stellar distances, and after defining distance complete samples between 1.2 and 3 kpc, we can trace the density distribution in the anticenter direction, finding a clear overdensity around 1.7 kpc with an amplitude of ∼10% that can be associated to the Perseus arm. Those distance complete samples, having a statistical significant number of stars, built using the new model based method for distance estimation, show a significance of the Perseus arm peak overdensity larger than 3σ. Exponential fittings also allowed us to constrain the radial scale length of the young population of the Galaxy between 2.0 and 2.6 kpc, as well as to estimate the stellar density at the solar vicinity for stars between B4 and A1 in ∼0.022 /pc2, well in agreement with the results obtained in the new version of the Besan¸con Galaxy Model. In addition, all these data allow the creation of a 3D extinction map, that carefully analyzed shows the presence of a dust layer clearly in front of the location of the stellar overdensity of the arm, suggesting that the corotation radius of the spiral pattern is further away of the position of the Perseus arm. The detection of this dust lane supports the existence of a density wave. Definitive confirmation will come from the ongoing spectroscopic survey using WYFFOS at the William Herschel Telescope in order to obtain radial velocities for a large subsample of the stars in our photometric catalog, that will allow us to trace the possible kinematic perturbation due to the presence of the Perseus arm.

13 14 Contents

IINTRODUCTION 19

1 The Milky Way spiral arms 21 1.1Morphology...... 21 1.2Anoverviewofthespiralstructuretheories...... 22 1.3Observationalconstraintssupportingtheories...... 24

2 The Galactic anticenter 25 2.1ThePerseusarm...... 25 2.2Thelargescalestructure...... 26 2.3Surveys&catalogs...... 28 2.3.1 IPHAS...... 28 2.3.2 2MASS...... 29 2.3.3 LAMOST...... 29 2.4Extinctionmaps...... 30 2.4.1 FroebrichExtinctionmap...... 30 2.4.2 Dark clouds from Dobashi et al. (2005) ...... 30 2.5Otherstudies...... 31

3 Thesis aims and methodology 33 3.1Photometricsurvey...... 33 3.2Physicalparametersandstarselection...... 34 3.3ThestellaroverdensityandthedustlaneassociatedtoPerseus...... 34

II A NEW PHOTOMETRIC CATALOG 37

4 The Str¨omgren photometric survey at the anticenter 39 4.1Surveystrategy...... 39 4.2Observations...... 40 4.3Datareduction...... 42

15 16 CONTENTS

4.3.1 DataPre-reduction...... 42 4.3.2 Photometryextraction...... 42 4.3.3 Extinctioncorrection...... 43 4.3.4 Transformationtothestandardsystem...... 43 4.4Finalcatalog...... 44 4.4.1 Meanmethod...... 44 4.4.2 Photometricprecision...... 46 4.4.3 Astrometricprecision...... 46 4.4.4 Limitingmagnitudeandsaturation...... 47 4.4.5 Illuminationcorrection...... 49 4.5Secondcalibration...... 49 4.5.1 Method...... 53 4.5.2 Newaccuracy...... 56

III STELLAR PHYSICAL PARAMETERS 61

5 Empirical calibrations 63 5.1Classiﬁcationmethods...... 64 5.2Extinctionandabsolutemagnitudecomputation...... 67 5.2.1 Earlyregion:O-B9typestars...... 67 5.2.2 Intermediateregions:A0-A3typestars...... 69 5.2.3 Lateregion:A4-A9typestars...... 70 5.3Eﬀectivetemperatureandotherphysicalparameters...... 70 5.4Errorcomputation...... 71

6 The new strategy: Model Based method 73 6.1Modelatmospheres...... 73 6.2Interpolationmethod...... 76 6.3Stellarevolutionarytracks...... 77 6.4 The role of metallicities ...... 79 6.5Binarityeﬀect...... 82 6.63Dﬁttingalgorithm...... 85 6.6.1 Method1:Gaussianweightedmean...... 85 6.6.2 Method2:Minimumdistance...... 86 6.6.3 Method 3: Maximum probability ...... 86 6.6.4 Method 4: Weighted maximum probability ...... 88 6.7Errorcomputation...... 90 CONTENTS 17

7 Testing distance derivation using Hipparcos data 91 7.1TheHipparcossample...... 91 7.2Classiﬁcationmethods...... 92 7.3Distancemethods...... 94 7.3.1 Empiricalcalibrationmethods(EC)...... 96 7.3.2 Comparingfordiﬀerentatmosphericgrids(MBmethod)...... 101 7.4Comparingmodelbasedandempiricalcalibrationmethods...... 108 7.5Conclusions...... 111

8 Application to our catalog 113 8.1MBmethod...... 113 8.1.1 Probability ...... 113 8.1.2 Physicalparameters...... 115 8.1.3 Errors...... 116 8.2ECmethod...... 117 8.2.1 Physicalparameters...... 117 8.2.2 Errors...... 117 8.3ComparisonbetweenECandMBmethods...... 123 8.4IPHAS...... 128 8.52MASS...... 129

IV THE PERSEUS SPIRAL ARM 133

9 Stellar content in the anticenter 135 9.1Thecatalogofyoungstars...... 135 9.2Limitsonapparentmagnitude...... 138 9.3Lookingforapopulationcompleteupto3kpc...... 139

10 The spiral arm overdensity 145 10.1Methodology...... 145 10.1.1Derivationoftheoptimalbinwidth...... 145 10.1.2Computationofthestellarvolumedensity...... 146 10.1.3Computationofthestellarsurfacedensity...... 147 10.1.4Externalobservationalconstrains...... 149 10.2Radialdistribution...... 151

10.2.1 Degeneracy hz − Σ ...... 152 10.2.2Radialscalelength...... 153 18 CONTENTS

10.3ThePerseusarmoverdensity...... 155

11 The spiral arm dust layer 159 11.1Extinctionmapintheanticenter...... 159 11.2Froebrichextinctionmap...... 160 11.3ThePerseusdustlayer...... 163

11.4 Irregularities in the AV distribution...... 164

12 Towards the detection of the kinematic perturbation 169 12.1Simulatingtheexpectedkinematicperturbation...... 169 12.2ObservationalradialvelocityprogramwithWYFFOS@WHT...... 170 12.3FirstattemptusingLAMOSTdata...... 171

13 Summary, conclusions and future perspectives 173 13.1Summaryandconclusions...... 173 13.2Improvementsandfutureperspectives...... 176

ATables 177

B MV calibration for each spectral type 187

C Surface density distribution plots 189

D Changing the stars in the gap 203

E Bibliography 205 Part I

INTRODUCTION

Chapter 1

The Milky Way spiral arms

The Galaxy is a system of about 1011 stars, interstellar gas and some small quantities of dust, where magnetic fields are present, and cosmic ray particles move along the field lines. But the main forces governing the structure and kinematics of the system are gravitational. Superposed on this background distribution we can find the spiral structure, which seem to be organized across the largest parts of the Galaxy although local details are irregular and disrupted. It has been more than 150 years since William Parsons (1800-1867), the third Earl of Rosse, identified the spiral structure of M51 in 1845. However it was not until 1952 when Morgan et al. (1952) found evidences for a spiral structure in the Milky Way. They used the distribution in space of the nearer regions of ionized hydrogen, analyzing them through spectroscopic parallaxes. Meantime, Ewen & Purcell (1951) studied the emission in the 21 cm line in our Galaxy, and they could extend the evidences of these spiral features for further distances from the Sun. Many years after that, although it is well established that spiral arms are important agents driving the evolution of the galactic disks (Sellwood 2011; Fujii et al. 2011), the observational evidences that describe the characteristics of the spiral arms in the Milky Way are frustratingly inconclusive (Lépine et al. 2011). Key questions are still open, some of them being: which is the mechanism of the formation and evolution of the spiral pattern in stellar disks?, are they transients or long-lived structures?, which are their building blocks: stellar or gaseous? This chapter present a non-exhaustive overview of the current state of the art, emphasizing the actual knowledge on the outer Perseus spiral arm in chapter 2.

1.1 Morphology

Basic structure parameters of the Milky Way, such as the number of arms, are still not clear: whereas maps of OB-associations and HII-regions (Georgelin & Georgelin 1976; Russeil 2003) and the Galactic distribution of free electrons (Taylor & Cordes 1993) suggests a 4-armed pattern, infrared surveys such as COBE K-band data (Drimmel 2000) propose that the non-axisymmetric mass perturbation has a two rather than a four armed structure. External galaxies often show a two-armed structure in near-infrared while they may appear multi-armed in visual bands (Grosbøl et al. 2004), indicating that diﬀerent arms could have diﬀerent building blocks. The spiral model of the Milky Way obtained with Spitzer/IRAC infrared data in the Galactic center direction (Benjamin 2008) is in agreement with this extragalactic scenario. Benjamin (2008)

21 22 CHAPTER 1. THE MILKY WAY SPIRAL ARMS

Figure 1.1: Left: Sketch by Vallée (2008) of the spiral arms of the Milky Way. Right: artistic view of the milky way developed by Robert Hurt and obtained from Churchwell et al. (2009). Spiral pattern proposed by Efremov (2010) is overplotted in both figures. proposes that the Milky Way has two major spiral arms (Scutum-Centaurus and Perseus) with higher stellar densities and two minor arms (Sagittarius and Norma) mainly filled with gas and pockets of young stars. Whereas Yáñez et al. (2008) proposed that these additional gas arms may form due to a secondary shock in a 2-armed spiral perturbation, Englmaier & Gerhard (1999) associated them to the response of the bar perturbation. We can see this distribution in Fig.1.1, where Vallée (2008) shows a possible distribution of the arms and we can also see the artistic view of the Milky Way developed by Robert Hurt, with the name and location of the arms according to Efremov (2010). The pitch angle (usually associated to logarithmic spiral arms) has been ranging from 12◦ (e.g., Drimmel et al. (2003) or Russeil (2003)) to 5◦ (Melnik 2003). Other parameters like interarm separation, amplitude of the arm overdensity, and even live-times of the arms are also under discussion. The derivation of most of these parameters is associated to the spiral arm theory adopted for the analysis. These models provide physical relations between them and also try to explain the origin and evolution of the spiral structures. In Vallée (2005) we can find a very detailed review of different studies about the Milky Way spiral arms made by different authors and using different data (HII regions, CO clouds, stars, OB associations, dust, etc.). Combining all these data, they proposed a possible distribution and shape for the Milky Way spiral arms (see Fig.1.1). Hereafter, we will use the nomenclature from the Vallée (2008) picture for the spiral arms names.

1.2 An overview of the spiral structure theories

It is not surprising that rotating disk galaxies should exhibit spiral structure, but the nature of these spiral patterns is not completely understood, probably because the origin of this spiral structure is not unique. Are the spiral arms of the Milky Way material arms or density waves? The answer to this question is still a great challenge of Galactic astronomical research. The disk galaxies rotate differentially, so the orbital period increase with the radius R.Thusifspiral 1.2. AN OVERVIEW OF THE SPIRAL STRUCTURE THEORIES 23 arms were long lived material features, then differential rotation would wind them up into very tightly wrapped spirals. Early in the sixties, Lin & Shu (1964) suggested a new theory named density wave theory, with a spiral density wave traveling through the galactic disk. So while rotating through the disk with a constant angular speed, the stars and the gas pass through the arms, the potential well would increase, increasing also the star density and the star formation. Lin & Shu theory assumes that the spiral structure is a stationary density wave, and it remains unchanged over many orbital periods. However, this assumption may not be true, and most evidences show that spiral patterns change over the time. In addition, this theory do not discuss the origin of the spiral pattern. Another related mechanism is the one proposed by Toomre, also assuming a spiral density wave theory. As known, disks are stabilized on small scales by random motion, and on large scales by rotation, although random motion can be temporarily suppressed. In those cases, small perturbations in the disk can be swing amplified as described in the so-called swing amplification theory (see Toomre (1981)). Masset & Tagger (1997) proposed an extension of this theory taking into account the non linear effects, this is the so called resonant coupling theory. Using this extension it is possible to understand the formation of galactic systems with more complex spiral arm morphologies. A very different approach was presented by Romero-Gómez et al. (2007), proposing a dynamical theory for the spiral arms, with its origin in the periodic orbits around the equilibrium points of the galactic system. The invariant manifolds associated to the unstable periodic orbits around these equilibrium points form rings or spiral features that, depending on the bar and disk parameters, can match the observational constraints. While for the other theories the stars move across the arms, the invariant manifold theory suggests that the stars populate these spiral shape orbits, so the mean motion would be along the arm. The stars kinematics is a clear observational constraint that would distinguish between this and other theories. Another alternative is based on external interactions. Sellwood & Carlberg (1984) presented simulations in which the disk grows through gas accretion, with the accreted mass being added to the model in the form of particles on initially circular orbits. If the accreted mass per rotation is about 1.5% of the disk’s initial mass, the disk can maintain an open spiral pattern similar to the spiral patterns of Sc galaxies. Also tides from external galaxies provoke a two-sided response. For example, the two armed grand-design spiral galaxies M51 and M81 are clearly interacting with external companions, so it is very likely that these galaxies owe their symmetric spirals to these tidal interactions (Toomre & Toomre 1972). Other theories describe spiral disks supported by chaotic orbits (Voglis et al. 2006; Patsis 2006), important when the perturbations are large, specially near corotation. This chaotic motion creates spiral arms almost completely formed by mass. These different models do not have to be mutually exclusive. The most critical issue nowadays is to improve the observational evidences to test them. Nowadays as the observational data available has not enough accuracy to test these theories, numerical simulations are commonly used. Orbits integration in a fixed potential (test particle simulations) and self-consistent N-body simulations are being used to study the spiral arm properties and their formation and evolution. From simulations it has been found that the spirals perturb strongly the kinematics of the disk (Antoja et al. 2011) and that the amplitude, pitch angle and pattern speed profile of the spirals give a lot of information about their nature 24 CHAPTER 1. THE MILKY WAY SPIRAL ARMS

(Roca-F`abrega et al. 2013).

1.3 Observational constraints supporting theories

External galaxies are a perfect test bed to study possible spiral theories. As mentioned before, the derivation of the pattern speed of a spiral perturbation is an important physical parameter to disentangle between theories. An efficient method to compute pattern speeds in external galaxies is the method from Tremaine & Weinberg (1984) that uses spectral and photometric information in long slit spectra across the galactic disk. Also in this line, and as an example of the recent observational efforts, Buta & Zhang (2011) proposed and applied a new method, named ‘potential-density phase-shift method’for locating corotation radii in external galaxies. The authors prove that numerical simulations have been very useful for highlighting the impact of pattern speed on galaxy structure. The tool allows the determination of the kinematic properties of galaxies using their galaxy morphology. However, although this observational programme shows interesting results such as the fact that multiple pattern speeds are common in spiral and barred galaxies and that both bar-driven and non-bar-driven spirals are detected in a large sample of more than 150 galaxies, one of the important requirements of the method is that wave modes in galaxies shall be quasi-stationary. Thus, the conclusions of this huge observational effort rely in a hypothesis that has not been tested. On the other hand, and as pointed out by Rix & Rieke (1993), observationally, density wave phenomena can be best studied in the near infrared. K band images of face-on galaxies do trace the massive disk star population and allow a mapping of the azimuthal variation in the surface mass density of the stellar disk. But again, questions rise: the spatial structure seen in the near-IR, and the star formation, seen in the optical bands, are coupled or not? Are the dynamics and the star formation related? How this is linked to the spiral structure theories? Observational programmes are ongoing to analyze how the spiral density wave is triggering the star formation (i.e. Mart´ınez-Garc´ıa et al. (2009)). Grosbøl (2006) and Grosbøl & Dottori (2012) analyzed both the azimuthally distribution of young stellar clusters (Age< 7 Myr) and the age gradient of clusters across the spirals. The fact that young, massive clusters show azimuthal age gradient suggests the presence of density wave in NGC 2997. As discussed in Grosbøl (2013) other observational tracers can be: 1) the dust lanes (outlined in (B-K) colour index maps), 2) the derivation of amplitude and pitch angle in spirals, that would suggest a lower limit in the radial force, 3) the colour gradients along the arms, that would trace the star formation process after large-scale shock, among others. These are only few examples of the huge observational efforts in progress focused to distinguish among the different spiral scenarios, programmes designed both to test the validity of the theoretical models proposed and to disentangle the nature of the spiral arms. However, up to now none of them have been conclusive for a definitive understanding of the Milky Way spiral scenario. Chapter 2

The Galactic anticenter

2.1 The Perseus arm

The Perseus arm has been studied mostly in the second and third Galactic quadrant. However there are very few studies linking both quadrants and providing information in the anticenter direction (i.e. at galactic longitude l = 180◦). This statement is inherent to the fact that distances from HI observations cannot be computed in this direction. This is observed in Fig.2.1- top-left reproduced from Levine et al. (2006). The authors exclude the region between 165◦ and 195◦, since in this direction the large scale velocities along the line of sight are too small with respect to their random velocities to establish reliable distance from the HI data.1 The Perseus spiral arm has been studied at different wavelength and using different tracers in the last decades. Almost fifty years from now, Lindblad (1967) undertook a deep kinematic analysis of the HI neutral gas in the anticenter. He pointed out the existence of large irregular and asymmetric motions with important departures from circular rotation of the gas motion, associating these irregularities to the distribution of matter in the spiral arms. More recently, Dame et al. (2001) published a new large-scale CO survey providing detailed information on individual molecular clouds. They found that a third-quadrant extension of the Perseus Arm is visible although it is traced by fewer and generally fainter clouds than in the second quadrant. A similar study was developed by Carpenter et al. (2000) in a multiwavelength analysis using the CO Survey, the IRAS Point Source Catalog, the published radio continuum surveys and new near-infrared and molecular-line observations. They studied the star formation properties of molecular clouds concluding that clusters around OB stars contribute substantially to the stellar population currently forming in the W3/W4/W5 HII regions within the Perseus arm. Russeil (2003) published an extended catalog of star forming complex. She determined the position, the systemic velocity and the kinematic distance for each of them, which allowed to trace the Perseus arm in the second quadrant. She concluded that in both, the three-arm and the four-arm fitted models, the Perseus arm is always unambiguously delineated. More recently, Xu et al. (2006) gave a distance of 1.95±0.04 kpc at the massive star-forming region W3OH (l = 134◦), that they locate in the Perseus arm. The same authors extended the study (Reid

1The method used to study the kinematics of the gas needs the assumption of a galactic rotation curve, and then through the radial velocity at diﬀerent directions, an estimation of the distance can be done, everywhere, except in the Galactic anticenter direction, where the radial velocity component due to the Galactic rotation is null.

25 26 CHAPTER 2. THE GALACTIC ANTICENTER et al. 2009) with up to ﬁve star-forming complexes between l = 112◦ and l = 189◦ in the Perseus arm located at distances between 1.95 and 2.81 kpc, from which they obtained a pitch angle for the Perseus arm of 16.5±3.1◦. The authors also locate two of the complexes at the outer arm (at distances of 5.3 and 5.9 kpc) with a possible pitch angle of 2.3◦. Brunthaler et al. (2011) extended the study obtaining similar results (see Fig.2.1). Emission line stars have recently been used to study the Perseus arm. Raddi et al. (2013) used IPHAS data and low resolution spectroscopy to select and characterize Be stars in the region 120◦

2.2 The large scale structure

Many different large scale features can be studied when observing in the anticenter direction, e.g. the radial and vertical scale length, together with the possible truncation of the disk (cut-off). Warp and flare have been also proved to be important. As pointed out by Freeman (1970) the scale length of the thin disk varies as a function of Galactic morphological type. It is a very poorly known parameter although it can be a major discriminant of theories on thin disk formation. For external galaxies the derivation of the radial scale length as a function of age is now being studied (e.g. Gogarten et al. (2010), for NGC300), finding evidences for inside-out growth of the stellar disk: the scale length increase from past (old stars) to present (young population). For the Milky Way, different values have been published when using different stellar population to study it. van der Kruit (1986) obtained 5.5±1.0 kpc using the surface brightness of the Galactic background in the Pioneer 10 background starlight experiment. Habing (1988) obtained a scale length of 4.5 kpc (and a cutoff at a galactocentric distance of 9.5 kpc) through the IRAS Point Source Catalog. K giants tracing the old disk where used by Lewis & Freeman (1989) to obtain the value of 4.4 kpc. Infrared radial surface 2.2. THE LARGE SCALE STRUCTURE 27

Figure 2.1: Different results of spiral arm studies. Top-Left: Figure from Levine et al. (2006), where a four-armed symmetric spiral model is overplotted, the solid lines represent the model over its claimed range of validity, the dashed lines are an extension beyond that range and the unlabeled short line near the Sun is the local Orion arm. Underlying contours indicate surface density of HI, with colored regions being overdense compared with the local median, whereas gray scale regions are underdense. Top-right: Plot from Russeil (2003) where circles are star- forming complexes with size proportional to the excitation parameter. A four arm model is over-plotted. Bottom-Left: Figure from Brunthaler et al. (2011) with an artistic plot of the Milky Way from R. Hurt. Overplotted we can see all the observed VLBA sources. Distance error bars (in green) are shown for all sources. Bottom-right: Figure from Vázquez et al. (2008) with the CO molecular clouds indicated in gray squares (their size indicate their mass), clusters indicated with open circles and blue plummes plotted with open circles. Spiral arms from Vallée (2005) are overplotted. 28 CHAPTER 2. THE GALACTIC ANTICENTER brightness allowed Kent et al. (1991) to compute also this value, obtaining 3.0 kpc. However, Robin et al. (1992) obtained a much shorter value of 2.5 kpc through CCD photometry in a low extinction area in the anticenter direction, result supported by Ruphy et al. (1996), that obtained hR=2.3±0.1 kpc using DENIS (infrared data in the southern sky), while Robin et al. (2003) provide 2.53±0.11 kpc. And using DIRBE data, Freudenreich (1996) obtained also a short scale length of 2.64 kpc. Siegel et al. (2002), again in the visible obtained 2-2.5 kpc, while Jurić et al. (2008), using SDSS data, computed for the thin disk hR=2.6 kpc. More recently, Sale et al. (2010) used IPHAS data to select early-A type stars in the anticenter direction. They fitted two exponential scale lengths (inner and outer) of 3.0 kpc and 1.2 kpc respectively. There still remain some uncertainty in the absolute value of the disk scale length(s). As discussed by Feast (2000) this uncertainty does not affect the conclusion that the disk scale length is varying with age. Kinematic determination of this parameter points towards a decrease in scale length when increasing velocity dispersion, thus when increasing the age of the population. However, several studies point out that the scale length may change at different galactocentric radius, giving slightly larger values at the outer part of the Galaxy. Many of these large scale studies also reveal the presence of a truncation of the disk at larger radii. Habing (1988) provided a value of 9.5 kpc (although he gave, a large value for the scale length hR=4.5 kpc) using IRAS point source catalog, Ruphy et al. (1996) obtained 15.0±2kpc, Robin et al. (1992) gave 14 kpc, while Sale et al. (2010) suggested 13 kpc. The effect of the warp is known to be small in the Galactic anticenter, since it is expected to be very close of the line of nodes. Momany et al. (2006) studied the warp through 2MASS red clump and red giant stars, obtaining the maximum of the warp at l ∼ 240◦, with the plane of the disk towards b ∼−0.5◦ in the anticenter direction. López-Corredoira et al. (2002) modeled −3 5.25 ◦ it following zW (pc) = 1.2 · 10 · R(kpc) · sin(φ +5 ), where R is the galactocentric radius in ◦ kpc, with R=7.9 kpc, and φ is the galactocentric longitude. So the line of nodes is just 5 from the anticenter, and the disk slightly up at l =180◦.AndReylé et al. (2009), provides another 2 model: zW (R)=27.4(R − RW ) sin(l)withRW =7 kpc being the galactocentric radius where the warp starts, and l the heliocentric galactic longitude, so with the lines of nodes just in the anticenter direction. As can be seen, the direction of the line of nodes is still a matter of debate. The Galactic flare is defined as the increase of the thickness of the stellar disk at large galactocentric radius. Momany et al. (2006) made a comparison of the thickness of the stellar disk, neutral hydrogen gas layer and molecular clouds. As commented by the authors the unexpected aspect of this comparison is very high outer gas scale height, apparently exceeding that of the stars beyond 20 kpc. This effect is not well understood.

2.3 Surveys & catalogs

Here we mention some of the recent large surveys with important contribution to the study of the anticenter direction.

2.3.1 IPHAS

The INT Photometric Hα Survey of the Northern Galactic Plane (IPHAS, Drew et al. (2005)) is a photometric survey developed with the Wide Field Camera at the Isaac Newton Telescope. They cover the Galactic plane (|b| < 5◦) with three ﬁlters (r’, i’, and Hα) up to a limiting 2.3. SURVEYS & CATALOGS 29

Figure 2.2: Equatorial map of the regions observed in the LAMOST pilot survey. Figure from Luo et al. (2012). The anticenter is at (α, δ)=(86.4◦, +28.9◦).

magnitude of r’=20. The Initial Data Release (IDR, Gonz´alez-Solares et al. (2008)) published part of the catalog and it is available via web.

2.3.2 2MASS

The Two Micron All Sky Survey (2MASS) (Skrutskie et al. 2006; Cutri et al. 2003) is a full sky catalog in the infrared that provides J(1.25μm), H(1.65μm), K(2.17μm) photometry for more than 4·108 stars. The magnitude limits reached are J=15.8, H=15.1 and K=14.3.

2.3.3 LAMOST

The Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST) (Cui et al. 2012) is a Schmidt telescope with 4000 optical fibers positioned in its 5◦ focal plane. It is devoted to a spectroscopic survey of 10 million objects with a wavelength between 370-900nm and a resolution of R=1800. The survey is divided in two main components: LAMOST extragalactic survey (LEGAS) and LAMOST Experiment for Galactic Understanding and Explotation (LEGUE) survey of the Milky Way. Inside LEGUE several targets are planned to be observed, i.e. the halo, the disk and also star clusters. The LAMOST pilot survey (Luo et al. 2012) finished in 2012. The data release provides spectra for more than 300000 stars. Part of the Galactic anticenter region was covered during dark nights, so they reach fainter magnitude limit r ∼[14.5,19.5] for those fields (see the distribution of the fields in Fig.2.2). In this release they provide radial velocity for the stars as well as the spectral type. As part of the LAMOST survey, there is the LAMOST Spectroscopic Survey of the Galactic Anti-center (LSS-GAC) covering |b| < 30◦ and 150◦

Figure 2.3: Froebrich et al. (2007) AV extinction map.

2.4 Extinction maps

2.4.1 Froebrich Extinction map

Froebrich et al. (2007) provides an extinction map in the Galactic anticenter region from 2MASS data. The 8001 ◦ area is covered between 116◦ and ). The median value is used in order to minimize the eﬀects of foreground and red young stars. The computed median for each region are compared with extinction free regions in order to obtain the excess for each region. These excess are transformed to AH andthentoAV using the Mathis (1990) reddening law (AV =5.689 × AH ). The resulting extinction map has a resolution of 4 and it is shown in Fig.2.3.

2.4.2 Dark clouds from Dobashi et al. (2005)

Dobashi et al. (2005) provide a catalog of dark clouds obtained through star counts in the optical database “Digited Sky Survey I”. All the Galactic plane |b| < 40◦ is covered. They provide the location of HII regions, supernova regions and 2D maps of the absorption in the visible AV for many diﬀerent regions, being their region 5 the one covering the anticenter. The AV maps are provided at two diﬀerent resolutions: 6 and 18. From the map, they located dark clouds and clumps, providing their extinction, location and extent (see Fig.2.4). 2.5. OTHER STUDIES 31

Figure 2.4: Figures from Dobashi et al. (2005). Left: location of HII regions (white circles) and supernova remnants (ﬁlled circles). Right: AV map in the anticenter direction.

2.5 Other studies

Several studies located different objects in the anticenter direction that will be interesting for our studies. For example, Reipurth & Yan (2008) developed a search for molecular clouds and star formation regions in the anticenter direction. According to these authors, this region hosts a number of massive molecular cloud complexes, some of them with currently active star formation. The AurOB1 association covers a large region in the sky, from l∼170◦ to l∼178◦ and b∼-7◦ to b∼4◦ and a distance of 1.32±0.1 kpc. On the other hand, Gemini OB1 covers longitudes from l∼188◦ to l∼191◦ and b∼-2◦ to b∼4◦ with two groups of stars, one at 1.2 kpc and the other at 2 kpc. In Fig.2.5 we reproduce their figure, that provides the location of the different star formation regions in these complexes. Other feature that called our attention is Simieis 147, a supernova remnant from an OB star that exploded 40000 years ago, with an extension of 3◦. In its center, the pulsar (PSR ∼ +0.42 J0538+2817) is located at (l,b) (179.7,-1.7) (see also Fig.2.5) and distance of 1.47−0.27 kpc (Reipurth & Yan 2008). Tovmasyan et al. (1994) provide photometry for up to 42 OB stars in these regions. And Negueruela & Marco (2003) provide spectra for some OB stars at large distances in this region, claiming that some of them could be in the Cygnus arm instead of close to the Perseus arm. Kim et al. (2000) studied the molecular clouds through star counts in four different directions slightly above the plane, all of them around l∼180◦ and b∼5.5◦. Their star counts function shows two peaks around 1.4 kpc and 2.7 kpc, with two molecular clouds at 1.1±0.1 kpc from the Sun. To obtain these results they assumed a luminosity function and a constant absorption of AV =0.8 mag/kpc. 32 CHAPTER 2. THE GALACTIC ANTICENTER

Figure 2.5: Figure 1 from Reipurth & Yan (2008) where we added in red the location of NGC1893. The (l,b) extinction map below is the level of extinction provided by Dobashi et al. (2005). Several star formation regions are located, as well as the limits of the complexes Gem OB1 and Aur OB1. Chapter 3

Thesis aims and methodology

The main goal of this thesis has been to quantify the stellar overdensity induced by the Perseus arm in the anticenter direction. For that, it is needed to trace the number of intermediate young stars as a function of the heliocentric distance expecting an overdensity when we cross the Perseus arm. As stellar tracers of the arm overdensity we have selected intermediate young stellar population that is the B5-A3 type stars. These stars are bright enough to reach large distances, and furthermore, they have the proper age to undertake the study, i.e. they are old enough so they have had time to feel the spiral arm potential perturbation (at least older than one rotation of the spiral pattern), and at the same time they are young enough so their intrinsic velocity is still small. It is well known that peaks in space density of very young OB-stars would mark current complexes of star formation while older populations like late-B or early-A type stars are expected to show a density variation due to the presence of a density wave. This also suggests (assuming a density wave theory) that their response to a wave is stronger, and thus their spiral amplitude. To study the Perseus arm we have to observe in the second and third quadrants. The anticenter direction was selected for diﬀerent reasons. First, and slightly depending on the pitch angle, this is in the range where Perseus arm is closest to the Sun. Then, this direction will allow us a better study of the kinematic perturbation in a future second step of the project. Since the projection of the large scale Galactic rotation on the line of sight direction is expected to be almost negligible for stars in circular orbits, radial velocities will directly allow us to detect the radial perturbation due to the presence of the arm. So by obtaining spectra of several of the stars of our survey, we should be able to detect the kinematic perturbation associated to the arm.

3.1 Photometric survey

We need accurate stellar distances for our young population, and the intermediate band uvbyHβ Strömgren photometry has demonstrated to be an excellent tool for that purpose. A large number of stars are needed to get a good statistical sample, so a large area has to be surveyed. The only large device with Strömgren filters available is the Wide Field Camera (WFC) at the Isaac Newton Telescope (INT) located at El Roque de los Muchachos, in La Palma. Using the Besan¸con Galaxy Model (BGM) (Robin et al. 2003) we computed the expected number of counts, and so the size of the area to be surveyed. The initial 8 square degrees

33 34 CHAPTER 3. THESIS AIMS AND METHODOLOGY suggested by BGM simulations, where ﬁnally increased with a second area covering up to 16 ◦ in order to increase the statistics for nearby bins. As will be seen in Chapter 4, our survey is almost complete up to a visual apparent magnitude of V =17 (that correspond to u ∼ 20mag). All the steps of the photometric reduction process have been deeply and exhaustively analyzed with the aim to minimize the error in stellar distance that would be propagated by undesired large errors in the photometric studies. Good quality of the astrometric data is also required to include our selected targets in the future spectroscopic survey using the multi-object spectroscopic techniques (WYFFOS, LAMOST, ...).

3.2 Physical parameters and star selection

The Strömgren indexes allow us the computation of physical parameters, being critical for the derivation of accurate photometric distances from visual absolute magnitude and interstellar absorption. As known, several empirical calibrations are available in the literature, being the most widely used the old calibrations published by Crawford in the seventies. These calibrations are based in Strömgren photometry and old parallax data for nearby field stars in the solar neighbourhood and few open clusters, objects with low interstellar extinction. The different calibrations are discussed in Chapter 5. Our aim has been to test this classical approach with a new method, developed in this thesis (see Chapter 6), based on stellar atmosphere and stellar evolution models from recent literature. As will be seen, this new method, although model dependent, has proved to be a good test to the classical approximation. Nowadays we have the advantage to compare the obtained photometric distances with the trigonometric parallaxes provided by Hipparcos. All this work provide us a good estimation not only of the internal error in distance derivation but also on the possible systematic biases induced by the calibrations, models, etc. More important, effects such us binarity or emission line stars have to be evaluated to have a real estimation of the distance accuracy when looking for the stellar position of the Perseus stellar overdensity. On the other hand, we also need a good indicator of the spectral type, or age of the star, in order to be able to select the stars useful for our study. We want to see whether an overdensity of young stars associated to this arm can be identified, so we need to select the so-called intermediate-young stars from physical parameters such us the effective temperature or the intrinsic colour indexes. Up to now, our list of observed stars is a sample complete in apparent magnitude. But to confirm or refuse the stellar overdensity induced by the Perseus arm, it is mandatory to built a sample complete in distance, that is complete up to about 3 kpc, to cover all the spatial distribution of the stellar component associated to the arm. This is not an easy job and several strategies have been followed in Chapter 9 to built a final sample useful for our purposes.

3.3 The stellar overdensity and the dust lane associated to Perseus

It is expected that the spatial distribution of the young stars in our sample will reflect several of the large scale features of the Milky Way Galactic thin disk. When trying to detect the stellar overdensity associated to Perseus, in Chapter 10 we will have to take into account the radial density profile, the position of the warp, the position of the Sun above the plane, etc. The stellar 3.3. THE STELLAR OVERDENSITY AND THE DUST LANE ASSOCIATED TO PERSEUS 35 overdensity will be quantified by estimating the surface density as a function of the galactocentric radius. As will be discussed, the value of this parameter for the young stellar population is at present very uncertain and, furthermore it will be correlated to the scale-height of the disk. This global scenario has to be treated properly to set the stellar overdensity associated to Perseus, and a good statistical analysis is critical and required. As proposed by Roberts in the seventies, we would expect a dust lane associated to the arm, which position -in front or behind the arm- would depend on the position of the corotation radius of the spiral pattern. This parameter is nowadays also very uncertain. As will be seen in Chapter 11 the 3D extinction map derived from our photometric survey can provide new insights on this key parameter. In a near future we plan to trace the kinematic perturbation by combining the photometric data obtained in this PhD thesis with an spectroscopic survey that will provide accurate radial velocities (a small perturbation is expected). In Chapter 12 we present the first steps towards this kinematic detection. We have undertaken a pilot programme using the WYFFOS@WHT multi-object spectrograph. Very preliminary results using the first LAMOST radial velocity data will be also discussed, that together with our accurate distances show very promising results. 36 CHAPTER 3. THESIS AIMS AND METHODOLOGY Part II

A NEW PHOTOMETRIC CATALOG

Chapter 4

The Str¨omgren photometric survey at the anticenter

Although many other applications will be possible, the main goal of this survey is to detect the possible overdensity due to the Perseus arm. So the observations were planned to optimize this objective. In Sects. 4.1, 4.2, and 4.3 we describe the survey as it was presented in the paper Mongui´o et al. (2013). After that, in Section 4.5, we discuss the reasons and the results of a second calibration that modiﬁed slightly the photometric indexes of the stars in the catalog.

4.1 Survey strategy

The Strömgren anticenter survey must fulfill several requirements in order to have the capability to detect a possible overdensity of young stars induced by the Perseus arm, expected to be at about 2 kpc (Xu et al. (2006)) in the anticenter direction. Important requirements are: 1) a limiting magnitude to allow the detection of young stars up to about 3 kpc; 2) a survey area large enough to include a statistically significant number of young stellar objects in the anticenter direction, and 3) precise photometry to derive Strömgren photometric distances beyond the Perseus arm. Stars with ages between 150 and 500 Myr (such as those with spectral types B5-A3) are the best population to study the possible overdensity due to the Perseus spiral arm, since they are young enough to still have a small intrinsic velocity dispersion (making them respond stronger to a perturbation), but they are also old enough to have approached a dynamic equilibrium with the spiral perturbation. Strömgren uvbyHβ photometry (Strömgren (1966)) is the natural system to identify this population and allows us to obtain accurate estimates of individual distances and ages. A statistically significant amount of stars in the photometric survey is needed, and they need to reach at least 3 kpc from the Sun, so the required limiting magnitude is V=16m. 6 to detect m an A0V star and V=17. 7 for an A3V star (assuming AV =1 mag/kpc). In order to select the survey area needed, Besan¸con galaxy model simulations were used (Robin et al. 2003). Since it is likely that our galaxy has a relative weak perturbation (i.e. ∼10% variation of the disk density), approximately 900 B5-A3 stars per radial 1 kpc bin are needed for a 3σ detection. Following the simulations, an 8◦ area is needed to achieve this number of stars. This is what

39 40 CHAPTER 4. THE STROMGREN¨ PHOTOMETRIC SURVEY AT THE ANTICENTER

Table 4.1: Central wavelength and FWHM of the filters used. uvbyHβw Hβn Central λ (nm) 348.0 411.0 469.5 550.5 486.1 486.1 FWHM (nm) 33 15 21 24 17 3 we call the central part of the survey. Since the volume covered in the nearby bins is small, and also due to saturation effects, the statistics for these bins are too small, so an extra area with brighter limiting magnitude was added, increasing the survey to 16◦. This surrounding area is named the outer part of the survey. Distances better than 25% are needed to identify a 500 pc spiral arm perturbation at 2 kpc distance. This requirement imposes an upper limit on the errors in the absolute magnitude and in the interstellar extinction, both parameters to be derived from the Strömgren photometry. The procedures proposed by Crawford (1978), Strömgren (1966) and Crawford (1979) allow us to compute the absolute magnitudes for early (B0-A0), intermediate (A0-A3) and late type (A3-F0) stars, respectively. We estimated, by simple error propagation, that errors in Hβ and m m c0 smaller than 0. 020 and 0. 035 result in distance errors between 25-15% for B5-A0 stars and 25% for A3 type stars. These values were computed assuming for the visual extinction (AV )an error smaller than 0m. 2. The error in other indexes, although playing a role in the classification process, have no significant contribution on the estimation of distance errors. Due to the Galactic warp, the Galactic plane is expected to be slightly below Galactic latitude b=0◦ in the anticenter direction (see Momany et al. (2006).) For that reason the center of the survey area was shifted down to b∼-0◦.5 in a low extinction region (Froebrich et al. (2007)).

4.2 Observations

The observations were conducted using the Wide Field Camera (WFC) at the Isaac Newton Telescope (INT) located at El Roque de los Muchachos in the Canary Islands. The WFC is a four-chip mosaic of thinned AR-coated EEV 4K×2K devices with pixels size of 0. 333 and an edge to edge limit of the mosaic of 34.2. The six filters used were Strömgren u, v, b, y, Hβw, Hβn (see the central wavelength and band width in Table 4.1). Pixel binning of 1×1andslow read-out mode were used for the observations, with a typical seeing of 1-1. 5. The WFC is the only wide-field facility in the northern hemisphere that offers the full set of Strömgren filters. Data from three different observing runs (2009A, 2010B, and 2011A) were used for the catalog, and data from 2010A were excluded due to cloudy conditions. We were also granted some director’s discretionary time (in 2009 and 2011), but owing to bad weather these nights were not successful. Our 16◦ observing area was divided in a grid of 5×12 WFC fields (see Fig. 4.1), with an overlap between them of 3 in order to check for field-to-field variations. A different observational strategy was followed for the central and outer regions. For each of the 27 central fields (see Fig. 4.1), three consecutive observations were obtained, with a shift of 10 between them, in order to detect cosmic rays and avoid bad pixels. Exposure times for each filter and observation are detailed in Table 4.2. The observations in the outer region, which includes 33 WFC fields, were planned to increase the statistics for nearby stars in the first kiloparsec distance bins. A single observation with shorter exposure times was conducted for each of these fields (instead of three observations with offsets as in the central region). 4.2. OBSERVATIONS 41

Figure 4.1: Plot of the 60 WFC fields observed. Red line shows the b=-0◦.5 plane. In green: central fields observed during 2009A run. Dark blue: central fields observed during 2010B run. Light blue: a central field observed during the 2011A run with a longer exposure time. Pink: outer fields observed during 2011A run with shorter exposure times and a single observation per field. The anticenter fields are named acij,wherei=1,...,5, and j=01,...,12.

Table 4.2: Dates for the observing runs and exposure times for each observation and filter for our program fields. Run Dates Photom. AC fields Exposure times (s) Calibration nights observed uvbyHβw Hβn fields 2009A 2009 Feb 12-16 2 12 100 40 40 30 40 200 NGC1893, ac308 2010B 2011 Jan 08-11 4 14 300 80 40 40 40 200 NGC1893, ac308, ac406, Praesepe 2011A 2011 Feb 16-17 2 1 720 120 100 100 100 720 ac406, Coma Berenices 33 120 40 30 30 30 120 42 CHAPTER 4. THE STROMGREN¨ PHOTOMETRIC SURVEY AT THE ANTICENTER

The calibration fields used for the transformation to the standard system are given in Table 4.2. The open cluster NGC1893 was observed several times during the first two runs. The central part of this cluster has Strömgren photometry available from Tapia et al. (1991) and Marco et al. (2001). To better control the transformation for each of the four WFC chips, several observations of this cluster were done, each time placing the center of the cluster in the center of each of the WFC chips. This strategy ensured that enough bright stars were available in each field, with about 50 stars per chip for the transformation to the standard system. These data were also used to calibrate other stars around the cluster, which were used as secondary standards. During the first observing nights, two anticenter fields were observed repeatedly (namely ac308 and ac406). After their calibration using NGC1893, they were used as deeper secondary standard fields in the following observing nights. The Coma Berenices (Peña et al. 1993; Crawford & Barnes 1969a) and Praesepe (Crawford & Barnes 1969b; Reglero & Fabregat 1991) open clusters were used as standard fields in some of the runs because they are older than NGC1893.

4.3 Data reduction

4.3.1 Data Pre-reduction

The images were reduced using several IRAF 1 tasks. First, original files were split into four different images, one for each chip, and the bias derived from the overscan areas was subtracted. Bad pixels were replaced by linear interpolation using the nearest good pixels through the fixpix task. The linearity correction proposed on the CASU INT web page2 was applied, as was the transformation factor from ADUs to electrons given in the manual. Flatfielding was applied using the sky flats obtained during the observational runs. A mask was also applied to avoid the vignetted corner of chip 3.

4.3.2 Photometry extraction

All the stars available in the images were located using the daofind routine. Using the PSF photometry to derive instrumental magnitudes was carefully investigated. But the high depen- dency on the parameters that define the quality of a particular photometric image (seeing, sky background, etc.) can lead to differences on the order of 0m. 02 to 0m. 03, so the PSF fitting method was rejected and the full survey was reduced using a homogeneous aperture-corrected photometry. Twelve different aperture radii provided twelve different magnitudes for each star. The daogrow algorithm was used to obtain the aperture corrections and the fitted radii. The final instrumental magnitudes were computed from the integration of the derived curve of growth. The positions in the J2000 coordinate system were determined using wcs and a fifth-order polynomial taking USNO-A2 (Monet 1998) as reference catalog.

1IRAF is distributed by the National Optical Astronomy Observatories, which are operated by the Association of Universities for Research in Astronomy, Inc., under cooperative agreement with the National Science Foundation (Tody (1986)). 2http://www.ast.cam.ac.uk/∼wfcsur/technical/foibles/index.php 4.3. DATA REDUCTION 43

4.3.3 Extinction correction

Our calibration fields (see Table 4.2) were observed at several airmasses each night. Fitting their differences in magnitude vs. the differences in airmass, the extinction coefficients for each night were obtained. An intermediate range of magnitudes for these stars was selected for the fit, avoiding the brightest and the faintest ones. The measurements with airmass differences smaller − − than 0.1 were also rejected. The fitted function was: xi xj = k(χi χj) for all the available pairs of measurements i = j from the same star where χ is the airmass for each measurement, and x indicates instrumental magnitudes. The extinction coefficients kx for each of the six filters (u, v, b, y,Hβw,andHβn) and night are listed in Table A.1, along with the ranges in airmass used. The extinction-corrected magnitudes and indexes (x) were then computed as

x = x − χ · kx. (4.1)

In the case of the Hβ extinction coefficients, we computed and applied the average of the values obtained for Hβw and Hβn. (As known, they are centered on the same wavelength.) This coefficient was applied independently to each filter, which allowed us to take the change in airmass between both exposures into account.

4.3.4 Transformation to the standard system

The photometry from our calibration fields (see photometric ranges in Table A.2) was used to obtain the transformation coefficients to the standard Strömgren system. Several equations with different color terms were checked in order to select those that minimize the errors and correlations between coefficients, and also to avoid insignificant terms. The selected set of equations were

y − Vcat = A1 + B1 · (b − y)cat, (4.2) (b − y) = A2 + C2 · (b − y)cat, (4.3) · − · c1 = A3 + B3 (b y)cat + C3 c1cat, (4.4) (v − b) = A4 + B4 · (b − y)cat + C4 · (v − b)+D4 · c1cat, (4.5) Hβ = A5 + B5 · (b − y)cat + C5 · (Hβcat − 2.8), (4.6) where the prime indicates instrumental extinction-corrected variables and the subscript cat indicates the standard values. The fitting equation in (v − b) was selected instead of m1, because m1 has a narrower dynamical range for young stars than (v − b). As discussed in Sect. 4.4, the magnitudes in some individual filters may be missing, especially in the u filter due to the need for very long exposure times. In this case Eqs. 4.5 and 4.6 had to be modified to avoid the c1 or (b − y) indexes like

(v − b) = A˜4 + B˜4(b − y)cat + C˜4 · (v − b), (4.7) Hβ = A˜5 + C˜5 · (Hβcat − 2.8). (4.8)

Equations 4.7 and 4.8 were only used when the initial Eqs. 4.5 and 4.6 could not be used because some exposure in an individual filter was missing. The obtained coefficients from each night are listed in Tables A.3 and A.5. Chip 3 has a slightly different behavior than the others, as can be 44 CHAPTER 4. THE STROMGREN¨ PHOTOMETRIC SURVEY AT THE ANTICENTER seen in coefficients A3andC5, possibly because it is vignetted. The errors in the photometric indexes are computed from direct error propagation of the coefficients and magnitudes. Cor- relations among extinction coefficients were taken into account, as well as correlations among coefficients for the transformation to the standard system. Since correlations between both sets have not been taken into account, our errors can be slightly overestimated. However, as our standards have a wide range in both airmasses and colors, the contribution for such correlations should be small.

4.4 Final catalog

4.4.1 Mean method

A catalog of 323794 individual measurements was compiled and is available through the CDS (the detailed content for each column is described in Table A.6). The astrometry for each individual measurement was computed as the mean of the coordinates derived from each of the filter images (six if all the magnitudes are available). Next, a crossmatching process was executed, assuming that two or more measurements belong to the same target if their angular separation was smaller than 3. This crossmatch radius was selected as the value that minimizes the number of outliers and maximizes the number of assignations, taking into account that it is around two to three times the size of the seeing. STILTS 3 tools were used for that purpose, which also allowed us to assign an identifier (ID) to each star. Finally a weighted mean was computed that yielded the final photometric indexes for each target. Details of these computations are 1) those photometric indexes derived from magnitudes having FWHM smaller than two pixels were rejected (assumed to be bad pixels or wrong measurements); 2) a weighted mean was computed, 2 where the weight applied was wi =1/σi ,andσi is the individual error for each index, computed with full propagation errors; 3) outliers were rejected using a 5σ rejection process, obtaining a final number of measurements different for each index (see Table 4.3); and 4) the weighted standard deviation and the error of the mean were computed for each index. The m1 index was computed from the weighted mean of the individual m1 measurements, so it is not a direct linear combination of the mean (v − b)and(b − y) indexes. The final right ascension and declination coordinates for each target were also computed following a similar procedure. Table 4.3 shows the number of stars with 1, 2, 3, or more measurements. In the outer region, most stars have only one measurement, while in the central region, stars have usually three measurements, but six or nine if they were in an overlap region. Stars in fields ac308 and ac406 were observed up to 20 times. For the stars with a single measurement, the internal standard deviation computed by error propagation in Eqs. 4.2 and 4.7 was assigned. For targets with two or more measurements, a flag indicating the coherence between them was computed for each index. This flag gives the number of inconsistent pairs according to a Student’s t-test (t > 90% was adopted). For the V magnitudes, 97% of the stars with more than one measurement have a flag equal to zero; that is, all the measurements are consistent. Similar percentages are obtained for the other indexes. The catalog with mean magnitudes and color indexes in the anticenter direction contains 96980 stars (also available through CDS), but not all of them have the full set of indexes. Table 4.4 shows the statistics of the final photometric data available. A flag with six binary digits

3Starlink Tables Infrastructure Library Tool Set, http://www.star.bris.ac.uk/∼mbt/stilts/ 4.4. FINAL CATALOG 45

Table 4.3: Number of stars for which mean magnitudes and indexes were computed using N individual measurements. N V (b − y) c1 (v − b) m1 Hβ 1 38740 38740 14353 24294 24294 33143 2 12688 12705 5647 8320 8322 11358 3 25859 25864 9139 15430 15429 22485 >3 17968 17946 6985 11336 11335 15961

Table 4.4: Statistics of the number of stars as a function of the photometric information available. stars V (b − y) c1 (v − b) m1 Hβ ﬂagIA 1725 -----× 000001 13259 ×× ----110000 624 ×× - ××- 110110 22632 ×× - ×××110111 22616 ×× ---× 110001 150 ×××××- 111110 35974 ××××××111111 96980 95255 95255 36124 59380 59380 82947

indicates the indexes available for each target. As can be seen in Table 4.4 the catalog contains 35974 stars with all available indexes. Nonetheless, it is important to emphasize that it contains, in addition, 22632 stars with all indexes except c1, 22616 stars with V ,(b − y)andHβ,etc. 4 Reading the last row in Table 4.4, it can be seen that we have about ∼6x10 stars with m1 measurements or ∼8x104 stars with Hβ index. Table 4.5 shows the spectral type distribution obtained by applying the procedure described in Figueras et al. (1991) to the set of 35974 stars with all photometric indexes. This distribution can be compared with the contents of the Hauck & Mermilliod (1998) catalog, a local volume sample. As expected, our catalog contains a higher percentage of targets belonging to the late type group due to the different limiting magnitude. No stars in common were found between the two catalogs. Our survey area overlaps with the area covered by the North Hemisphere IPHAS survey (González-Solares et al. 2008), with 54109 stars in common. This overlap between both catalogs is helpful for detecting stars with emission lines and peculiar features. GSC2 ID is also provided in the catalog and only ∼2% of the stars do not have GSC counterparts. In Table A.8, the first ten lines of the catalog are provided, with the description of all the columns in Table A.7.

Table 4.5: Fraction of stars in the catalog for each spectral type Early type Intermediate type Late type B0-A0 A0-A3 A3-F0 F0-G0 G0 → 12% 8% 18% 56% 6% 46 CHAPTER 4. THE STROMGREN¨ PHOTOMETRIC SURVEY AT THE ANTICENTER

0.06

V (b-y) 0.05 c1 (v-b) m1 Hb 0.04

0.03 error in photometric indexes 0.02

0.01

0 11 12 13 14 15 16 17 18 19 20 V magnitude

Figure 4.2: Photometric precision, computed as the error of the mean, as a function of V magnitude for the stars with more than one measurement. Lines for the V magnitude and the ﬁve standard indexes are plotted. Bins of 0m. 5 are used to compute the mean, and inside each bin, outliers are rejected using a 5σ clipping.

4.4.2 Photometric precision

The photometric precision obtained from the error of the mean in each of the indexes is shown in Fig. 4.2 as a function of V magnitude. For bright stars (V<16m), internal precisions below 0m. 01 were obtained for V and (b−y)andbelow0m. 02 for the other indexes. For fainter stars, the internal precision can reach up to 0m. 04-0m. 05. For stars with a single measurement, the error of the mean could not be obtained, so we plot the internal standard deviation computed by error propagation in Eqs. 4.2 and 4.7 (see Fig. 4.3). For stars brighter than V =12m the errors increase owing to saturation problems. The bump around V∼16-17m is due to some nights with bright sky conditions, leading to larger error in the instrumental magnitudes. The chip-to-chip variation was also checked using the stars observed several times on diﬀerent chips, i.e. in the overlap regions. Small variations were seen, but always less than the internal uncertainty. The typical oﬀsets between chips are smaller than 0m. 02.

4.4.3 Astrometric precision

The internal astrometric precision, computed as the error of the mean, is around 0. 02 (see Fig. 4.4), less than one tenth of the pixel size (0. 333). Figure 4.5 shows the comparison between our astrometry with J2000.0 coordinates from UCAC3 (Zacharias et al. 2010), GSC2.3.2 (Lasker et al. 2008), and USNO-A2. Differences up to 0. 2 with UCAC3 and GSC2.3.2 can be observed, as well as a small trend in V magnitude, more pronounced in USNO-A2. All these effects are explained by the different epochs of the three catalogs (1995-2000, 1988, and 1955 for UCAC3, GSC2, and USNO-A2, respectively). USNO-A2 J2000.0 coordinates were used for the astrometric calibration because it contains stars fainter than UCAC3. However, the mean 4.4. FINAL CATALOG 47

0.14 V (b-y) c1 0.12 (v-b) m1 Hb 0.1

0.08

0.06 error in the photometric indexes

0.04

0.02

0 11 12 13 14 15 16 17 18 19 20 V magnitude

Figure 4.3: Internal photometric standard deviation computed by error propagation in Eqs. 4.2 and 4.7, as a function of V magnitude for those stars with only one measurement. Lines for the V magnitude and the five standard indexes are plotted. Bins of 0m. 5 are used in order to compute the mean, and inside each bin, outliers are rejected using a 5σ clipping. epoch for USNO-A2 is 1955.0, and since proper motions are not available and cannot be taken into account, our coordinates do not contain the effect induced by the relative Galactic rotation in the anticenter direction with respect to the Sun. This effect does not depend on the distance to the star (assuming a flat rotation curve) and can reach 0. 2-0. 3 for differences in epoch of 50 years. Figure 4.5 shows that the dispersion increase from top to bottom, again due to the differences between the epochs of our observations and catalog positions. Furthermore, the decrease in the dispersion with increasing magnitude is explained by the effect of the intrinsic motion of the stars, stronger at short distances (so bright magnitudes). We used UCAC3 proper motions to check that the systematic trends disappear when the difference in epochs (2010-1995) is considered. As mentioned, USNO-A2 does not provide proper motions, so the effects were not corrected in our final astrometric data. We verified that these trends have no effect on the crossmatching between our catalog and GSC2.3.2, so the GSC ID is provided as additional information for the user.

4.4.4 Limiting magnitude and saturation

The limiting magnitude was computed as the mean of the magnitudes at the peak star counts in a magnitude histogram and its two adjacent bins, before and after the peak, weighted by the number of stars in each bin. We estimated that the limiting V magnitude computed with this simple algorithm provides the ∼90% completeness limit. This was conﬁrmed through the comparison of the V magnitude distribution of our catalog of stars with all available indexes with that of the full catalog containing all the stars with observed V magnitude (see Table 4.4). This second catalog can be considered complete at the limiting magnitude of the previous one. The limiting magnitude obtained is not the same for all the survey. Data for the outer area 48 CHAPTER 4. THE STROMGREN¨ PHOTOMETRIC SURVEY AT THE ANTICENTER

0.04

0.03

0.02

0.01 astrometric precision (arcsec)

0 11 12 13 14 15 16 17 18 19 20 V magnitude

Figure 4.4: Astrometric precision, computed as the error of the mean, as a function of V magnitude in right ascension (in red and ×) and declination (in green and ∗) computed for each 0m. 5 bin. Outliers (less than 5%) were rejected using a 5σ clipping in each bin.

0.8 0.6 0.4 0.2 0 -0.2 -0.4

our - UCAC3 (") -0.6 -0.80.8 0.6 0.4 0.2 0 -0.2 -0.4 our - GSC2 (") -0.6 -0.80.8 0.6 0.4 0.2 0 -0.2 -0.4

our - USNOA2 (") -0.6 -0.8 12 14 16 18 12 14 16 18 V magnitude

Figure 4.5: Comparison of our astrometry with those from GSC2.3.2 (top), UCAC3 (middle), and USNO-A2 (bottom). Left: differences in αcosδ. Right: differences in δ. In red, mean differences. Green dashed lines show 1σ ranges. All differences are in arcsec. 4.5. SECOND CALIBRATION 49 were obtained using shorter exposure times. Also for the fields in the central region, the limiting magnitude is slightly variable due to both observation strategy and weather conditions. Figure 4.6 shows its two-dimensional distribution. As mentioned, the catalog with all the available indexes is limited by the u magnitude. As can be seen in Fig. 4.6, our catalog of the 35974 stars with all indexes available reaches ∼90% completeness at V∼17m and V∼15m. 5 for the central and outer regions, respectively. Figure 4.7 shows the V magnitude histogram for the two main areas in our survey (the outer area and the central deeper region). In both cases the comparison between all the stars with available V magnitude and those with all indexes are provided.

4.4.5 Illumination correction

Since WFC covers a large field, the importance of the illumination correction must be checked, owing to different illumination of the CCDs. To do that, a field of stars was observed at several positions on the CCDs, and only the y filter was used since the illumination correction is not expected to be color dependent. All the computed instrumental magnitudes for each star, corrected for atmospheric extinction, were averaged to obtain a mean magnitude for each of them. The residuals between each individual magnitude and the computed mean magnitude were computed. Figure 4.8 shows the smoothed distribution for the residuals across the field of view of the WFC. A weak trend in right ascension was found, reaching values up to +/-0m. 02, which is below our general photometric errors. No significant trend was found in declination. The scatter of the data did not justify using anything higher than a second-order fit in right ascension: Δm = aα2 + bα + c. The results of the fit are a=-0.484±0.029 mag/deg2, b=- 0.159±0.008 mag/deg, c= 0.005±0.001 mag with residuals of 0.04 mag. This correction was applied to a test area with no significant change in the final mean magnitudes, except for a slight increase in the corresponding errors. Finally, the computed illumination correction was not applied.

4.5 Second calibration

When computing the physical parameters for the catalog stars (see Sect.6) we realized that several stars were located below the ZAMS in a Hβ-[c1] diagram (see Fig.4.9). That region belongs to subdwarfs, and the large amount of stars there is physically non-possible. The effect may be partially explained through observational gaussian errors, but the bias is too large for that. In addition we found several stars with too large Hβ values, that do not fit with their other photometric indexes. So this suggested that the Hβ values could be biased. We checked possible reasons for that and found some wrong calibration stars (e.g., emission line stars) in the primary standard list for the 2011 January 9 night. The night of 2011 January 9 was used to calibrate all the secondary standard fields of ac406, ac308 and also field stars from NGC1893. Any bias in the calibrations for this night will be translated to the rest of the survey through the secondary standards. In order to calibrate them, we used a list of primary standard stars from the fields of NGC1893 and Praesepe. Re-checking the Hβ fits developed we found 2-3 stars that could bias the fits, and were proved to be emission line stars according to Marco & Negueruela (2002). So we decided to re-check the standard list for NGC1893 and repeat the calibrations by removing the doubtful stars. 50 CHAPTER 4. THE STROMGREN¨ PHOTOMETRIC SURVEY AT THE ANTICENTER

19.5 31

19.0

30 18.5

18.0

29 17.5

DEC (deg) 17.0 28 16.5

16.0 27

15.5

26 89 88 87 86 85 84 83 RA (deg)

18.6 31

18.0

30 17.4

16.8 29 16.2 DEC (deg) 15.6 28

15.0

27 14.4

13.8 26 89 88 87 86 85 84 83 RA (deg)

Figure 4.6: Two-dimensional distribution of the limiting magnitude showing the 90% completeness level. Top: Catalog of the 95255 stars with V magnitudes available. Bottom: Subcatalog of the 35974 stars with all the indexes available (See Table 4.4) 4.5. SECOND CALIBRATION 51

10000

8000

6000

4000 Number of stars

2000

80000

6000

4000 Number of stars

2000

0 10 12 14 16 18 20 V magnitude

Figure 4.7: V magnitude histogram. In red, stars with available V magnitudes. In green, stars with all indexes available. Top: Stars from the central deeper area. Bottom: Stars from the outer area. 52 CHAPTER 4. THE STROMGREN¨ PHOTOMETRIC SURVEY AT THE ANTICENTER

0.02

0.3

0.2 0.01

0.1

0.0 0.00

DEC (deg) ¢

0.1

-0.01

0.2

0.3

-0.02

0.5 0.4 0.3 0.2 0.1 0.0 0.1 0.2

RA (deg) ¡

Figure 4.8: Illumination differences in magnitudes at different field positions. Black lines show the location of the four chips, and coordinates in degrees are centered on the central chip. The illumination differences at each position were computed as the Gaussian-weighted mean (with σ=0.1◦) of the residuals around each point.

Figure 4.9: Hβ vs. [c1]. In red, stars from the catalog. In black, empirical ZAMS from Crawford (1978) for B-type stars, Crawford (1979) for A-type stars, and Crawford (1975) for F-type stars. 4.5. SECOND CALIBRATION 53

4.5.1 Method

In order to re-do the standard calibrations we took into account two diﬀerent issues. First of all we used a diﬀerent criteria for the selection of the NGC1893 stars that will be included at the standard list. Then we also re-checked the equation to be used for the Hβ calibration.

Selecting standard stars from NGC1893

The available photometry for NGC1893 is from Tapia et al. (1991) (T91 from now on), Hauck & Mermilliod (1998) (H&M from now on), and Marco et al. (2001) (M01 from now on). In total, there are 130 stars that have available photometry from one or several sources. H&M uses the same values as in T91, except for two star that have wrong Hβ value. These stars will be rejected from the standard list. The 55 stars with only one measurement will also be rejected due to low statistics. There are two stars with photometric indexes available from both references T01 and M01 that are inconsistent. Since we do not know which of the two references gives the right values, we decided to reject them. We avoided also those stars with Hβ value larger than 3.0, since these values seem problematic. Finally, we also rejected those stars that are classified as pre-main sequence stars or emission line stars by Marco & Negueruela (2002). After a first calibration we also detected two stars with very large residuals that were removed of the standard list. The final list of stars contain 66 standards from NGC1893. For the stars with M01 and T91 data we compute the mean for each index, weighting the values by the number of measures from each source.

Checking the equation on Hβ

IntheEq.4.6useduptonowforHβ calibration we included a term in (b − y). Here we also test the results obtained by avoiding this (b − y) term, i.e. using the Eq.4.8 for all the stars (even if all the index are available). We compare in Table 4.6 the results of the three ﬁts for the Hβ equation:

1. Eq.4.6 with the old standard list. (OLD from now on).

2. Eq.4.6 with the new standard list. (NEW-A from now on).

3. Eq.4.8 with the new standard list. (NEW-B from now on).

In Table 4.6 we see the obtained coefficients in the three cases. We clearly see how the C5 coefficients are closer to unity when we use the new standard primary list. On the other hand, the color term coefficients look significant for most of the nights. However, the sigma does not seem to get significantly smaller by omitting the (b − y) term. In addition, the range in (b − y) of the primary standard list stars is significantly smaller than the final field stars in the catalog, as we can see in Fig.4.10. While the final catalog has stars with (b − y) values up to 1.5-2, the primary standards from NGC1893 only reach (b − y) up to 0.8 (however, secondary standard for NGC8193, ac406 and ac408 reach (b − y)=1.5). So during the primary calibrations we will be extrapolating the (b − y) ranges. For all these reasons we decided to finally avoid the B5 term and use Eq.4.8 for all the Hβ calibrations. In Fig.4.11 we can see the Hβ-[c1]forthethree options, and also the sub-samples with low errors in all the photometric indexes. The selected 54 CHAPTER 4. THE STROMGREN¨ PHOTOMETRIC SURVEY AT THE ANTICENTER option is giving less bias, so less stars below the ZAMS. We will see in Sect.4.5.2 that this option is giving also better internal accuracy. 4.5. SECOND CALIBRATION 55 R2 σ 0.0040.004 0.0210.003 0.021 0.953 0.003 0.018 0.952 0.018 0.967 0.005 0.971 0.005 0.0110.005 0.013 0.985 0.005 0.012 0.986 0.013 0.989 0.005 0.987 0.005 0.0110.005 0.013 0.984 0.005 0.012 0.985 0.012 0.988 0.018 0.988 0.020 0.0270.018 0.030 0.925 0.020 0.026 0.906 0.028 0.929 0.005 0.913 0.006 0.0180.005 0.023 0.965 0.005 0.019 0.954 0.019 0.969 0.010 0.964 0.007 0.0190.007 0.018 0.947 0.007 0.018 0.975 0.016 0.973 0.014 0.977 0.010 0.0190.012 0.018 0.942 0.011 0.019 0.973 0.016 0.968 0.011 0.973 0.007 0.0180.008 0.017 0.952 0.008 0.018 0.977 0.017 0.974 0.973 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± 0.0010.001 0.962 0.001 0.910 0.000 0.998 0.969 0.0010.001 0.976 0.001 0.931 0.001 1.023 0.961 0.0010.001 0.982 0.001 0.940 0.001 1.029 0.961 0.0020.003 0.978 0.002 0.955 0.003 1.038 0.969 0.0010.001 0.966 0.001 0.938 0.001 1.027 0.957 0.0020.001 0.946 0.001 0.941 0.001 1.035 0.963 0.0020.001 0.922 0.002 0.918 0.002 1.024 0.955 0.0020.001 0.959 0.001 0.924 0.001 1.030 0.976 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± A5 C5 2.324 2.308 2.331 2.322 2.311 2.283 2.322 2.304 2.323 2.307 2.308 2.303 2.316 2.306 2.314 2.302 2.322 2.313 2.320 2.306 2.329 2.315 2.322 2.305 2.302 2.289 2.302 2.279 2.301 2.292 2.310 2.289 R2 σ 0.0050.005 0.0210.005 0.021 0.954 0.003 0.018 0.952 0.018 0.967 0.005 0.971 0.005 0.0110.005 0.013 0.985 0.006 0.012 0.985 0.012 0.989 0.006 0.988 0.006 0.0110.006 0.013 0.985 0.006 0.012 0.985 0.012 0.988 0.019 0.988 0.022 0.0270.019 0.030 0.926 0.021 0.027 0.908 0.028 0.925 0.006 0.913 0.006 0.0180.006 0.022 0.965 0.006 0.019 0.955 0.019 0.969 0.010 0.965 0.008 0.0190.008 0.018 0.948 0.008 0.018 0.976 0.016 0.974 0.017 0.977 0.011 0.0190.013 0.019 0.942 0.012 0.019 0.971 0.016 0.968 0.012 0.974 0.007 0.0180.009 0.017 0.952 0.009 0.018 0.977 0.017 0.974 0.973 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± equations in the three cases. 0.0030.003 0.955 0.003 0.887 0.002 0.975 0.956 0.0020.003 0.966 0.003 0.900 0.004 1.013 0.959 0.0020.003 0.974 0.003 0.918 0.004 1.020 0.960 0.0120.015 0.967 0.013 0.933 0.013 1.030 0.966 0.0030.003 0.960 0.003 0.894 0.003 1.005 0.942 0.0050.005 0.924 0.004 0.912 0.005 1.017 0.954 0.0110.008 0.906 0.009 0.887 0.012 1.011 0.942 0.0060.005 0.944 0.006 0.895 0.007 1.021 0.974 Hβ ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± 2011Jan08 2011Jan09 2011Jan10 2011Jan11 2011Feb16 2011Feb17 2009Feb 16 2009 Feb 13 0.0020.001 -0.018 0.001 -0.037 0.001 -0.029 -0.023 0.0010.002 -0.025 0.001 -0.042 0.002 -0.023 -0.007 0.0010.002 -0.020 0.001 -0.037 0.002 -0.024 -0.003 0.0050.005 -0.025 0.005 -0.036 0.005 -0.022 -0.005 0.0010.002 -0.017 0.002 -0.054 0.002 -0.033 -0.022 0.0030.003 -0.036 0.002 -0.051 0.003 -0.035 -0.014 0.0050.004 -0.031 0.005 -0.050 0.005 -0.030 -0.024 0.0030.003 -0.030 0.003 -0.045 0.003 -0.022 -0.004 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± A5 B5 C5 2.330 2.319 2.341 2.329 2.318 2.297 2.329 2.306 2.329 2.319 2.315 2.304 2.324 2.318 2.320 2.303 2.327 2.333 2.331 2.314 2.342 2.334 2.335 2.311 2.312 2.307 2.313 2.289 2.311 2.309 2.316 2.290 R2 σ 0.0040.004 0.0200.004 0.021 0.960 0.003 0.017 0.955 0.018 0.969 0.004 0.967 0.005 0.0120.006 0.015 0.986 0.005 0.012 0.980 0.013 0.988 0.005 0.985 0.005 0.0120.006 0.013 0.985 0.005 0.014 0.984 0.013 0.983 0.025 0.987 0.026 0.0370.026 0.036 0.831 0.027 0.032 0.860 0.039 0.884 0.004 0.829 0.005 0.0150.005 0.020 0.975 0.004 0.016 0.968 0.016 0.978 0.009 0.974 0.007 0.0190.008 0.017 0.946 0.007 0.019 0.979 0.016 0.972 0.018 0.976 0.012 0.0200.013 0.020 0.927 0.013 0.019 0.970 0.018 0.968 0.011 0.966 0.008 0.0200.009 0.021 0.941 0.010 0.022 0.967 0.018 0.961 0.968 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± Table 4.6: Coefficients for the fits in the Eq.4.6, old Eq.4.6, new Eq.4.8, new 0.0030.003 0.843 0.002 0.873 0.002 0.901 0.857 0.0020.003 0.856 0.003 0.844 0.004 1.003 0.843 0.0020.003 0.866 0.003 0.875 0.004 0.998 0.847 0.0170.018 0.860 0.016 0.882 0.018 1.015 0.854 0.0030.003 0.858 0.003 0.888 0.003 0.939 0.843 0.0050.005 0.838 0.005 0.886 0.005 0.959 0.828 0.0130.011 0.831 0.009 0.883 0.014 0.950 0.823 0.0070.008 0.849 0.007 0.871 0.008 0.936 0.846 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± 0.0020.001 -0.035 0.001 -0.046 0.001 -0.047 -0.045 0.0010.002 -0.047 0.002 -0.080 0.002 -0.036 -0.044 0.0020.002 -0.043 0.002 -0.065 0.002 -0.042 -0.039 0.0070.007 -0.048 0.006 -0.067 0.007 -0.036 -0.037 0.0010.002 -0.033 0.001 -0.054 0.001 -0.048 -0.039 0.0030.003 -0.053 0.003 -0.071 0.003 -0.057 -0.045 0.0070.006 -0.024 0.005 -0.046 0.007 -0.053 -0.040 0.0040.005 -0.049 0.004 -0.054 0.005 -0.056 -0.028 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± A5 B5 C5 2.330 2.328 2.343 2.332 2.332 2.320 2.350 2.322 2.330 2.324 2.324 2.306 2.324 2.323 2.326 2.303 2.322 2.333 2.328 2.310 2.340 2.340 2.338 2.314 2.307 2.314 2.323 2.293 2.295 2.303 2.311 2.275 c 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 1 1 1 1 1 1 1 1 56 CHAPTER 4. THE STROMGREN¨ PHOTOMETRIC SURVEY AT THE ANTICENTER

400

350 20 300

15 250

200 10 150

100 5 50

0 0 0.0 0.5 1.0 1.5 2.0 0.0 0.5 1.0 1.5 2.0

(b y) (b y)

£ £

180 20000 160

140 15000 120 100 10000 80 60 40 5000 20 0 0 0.0 0.5 1.0 1.5 2.0 0.0 0.5 1.0 1.5 2.0

(b y) (b y)

£ £

Figure 4.10: (b−y) ranges for primary NCG1893 (green), secondary NGC1893 (blue), secondary ac308 (yellow) and the full anticenter catalog (red).

Diﬀerences between catalogs

We present in Fig.4.12 the differences between the photometric indexes of the three versions of the catalog. The differences between the old and the new versions are plotted for V ,(b − y), c1, (v − b)andm1 while for the Hβ value we have the differences between the three versions OLD, NEW-A and NEW-B. The differences for the V magnitude reach around 0.03 and are slightly biased. The differences for (b − y) reach 0.02-0.03, as well as for c1.For(v − b)andm1 the differences can be slightly larger, reaching 0.08 for some stars. Finally, for Hβ the differences between old and new catalogs can reach 0.06 while the differences between the two new versions reach around 0.04.

4.5.2 New accuracy

With these new calibrations, the photometric accuracy shown in Figs. 4.2 and 4.3 are slightly diﬀerent, specially for the Hβ index. In order to analyze the changes we study the behaviour of the three versions of the catalog in diﬀerent cases:

• N=1: stars with only one measurement for the current index. In that case the photometric standard deviation computed by error propagation is plotted. These errors come from the instrumental photometric errors and the errors from the extinction and calibration coefficients. In this case, the differences between the catalogs are due to the different standard calibration coefficients (instrumental magnitudes errors and extinction coefficients are always the same).

• N>1: stars with more than one measurement in the current index. Here the error of the mean between all the measurements is plotted. So we are checking the internal accuracy of the catalog. 4.5. SECOND CALIBRATION 57

Figure 4.11: Hβ vs. [c1] for the old photometric catalog (red), the new catalog using the new standard list with the (b − y) term (blue) and the new catalog with the new standard list and without the (b−y) term in the equations (green). Top: All the stars from the catalogs. Bottom: Only the stars with errors in all photometric indexes smaller than 0.02. Black lines show the empirical ZAMS from Crawford (1978) for B-type stars, Crawford (1979) for A-type stars, and Crawford (1975) for F-type stars.

• N=3: stars with three measurements. All the observations for these stars will be observed consecutively during the same night, with a small shift between them, so probably with the same chip. In this case we are checking the internal accuracy during the same night and chip.

• N>6: stars with more than six measurements. These are stars with observations from diﬀerent nights, or located at the corner of the chips, so due to the overlap they are measured several times with diﬀerent chips. Here we are checking internal consistency between nights and chips.

The mean accuracies for all the indexes, catalogs and number of measurements are in Fig.4.13. We can reach diﬀerent conclusions looking at this ﬁgure:

• For N=1, i.e. standard deviation from the error propagation, we see that the results do not change much. Since the transformation coeﬃcients and their errors are slightly diﬀerent, we see small variations, e.g., accuracies in Hβ are slightly smaller for the new reductions, as well as for c1. On the other hand, accuracies for m1 and (v − b) are slightly larger.

• For N>1 we plotted the error of the mean for all the available measures, and we see a clear decrease of the Hβ uncertainties, so now the internal consistency for this index is much better. For NEW-A catalog the accuracy already improved. However the big decrease is for NEW-B catalog. Since in that case the (b − y) term was not used, the internal error is deﬁnitively better. The accuracy for other indexes remain pretty similar. In this case we have stars observed during the same night three times (or six, or nine if they are in 58 CHAPTER 4. THE STROMGREN¨ PHOTOMETRIC SURVEY AT THE ANTICENTER

Figure 4.12: Photometric diﬀerences between the old and the new catalog for the V magnitude and the six photometric indexes. For Hβ we plot the three diﬀerences between the OLD, NEW-A and NEW-B versions. 4.5. SECOND CALIBRATION 59

Table 4.7: Number of stars for which mean magnitudes and indexes were computed using N individual measurements. New reduction without (b − y)term. N V (b − y) c1 (v − b) m1 Hβ 1 38740 38740 14353 24294 24294 33143 2 12690 12710 5646 8322 8322 11348 3 25859 25857 9118 15427 15430 22489 >3 17966 17948 7007 11337 11334 15967

overlap regions) and also stars observed during diﬀerent nights. In order to study them separately the two other sets of plots are developed, i.e. for N =3 and N>6.

• For the N=3 group we have mainly stars observed three times during the same night and chip. We see that the error in Hβ decrease again. So the internal consistency within the same night and chip seems to improve.

• Likewise, for N>6 we also see an improve for Hβ accuracy, indicating a better consistency between diﬀerent nights and chips.

• In all cases we see an improvement of the internal accuracy of the Hβ index for the new reduction, giving slightly better results when the (b − y) term index is avoided. This conclusion agrees also with the selection of the NEW-B version of the catalog.

Since now the photometric indexes are slightly different with this new reduction, the number of rejected measurements when doing the mean can be slightly different, so the final number of measurements shown in Table 4.3 have slightly changed. We show the new results in Table 4.7. 60 CHAPTER 4. THE STROMGREN¨ PHOTOMETRIC SURVEY AT THE ANTICENTER 1 1 V (b-y) c (b-v) m Hb 19.0 19.0 19.0 18.5 18.5 18.5 18.0 18.0 18.0 17.5 17.5 17.5 17.0 17.0 17.0 N>6 16.5 16.5 16.5 V magnitude 16.0 16.0 16.0 15.5 15.5 15.5 15.0 15.0 15.0 14.5 14.5 14.5 0.025 0.015 0.005 0.025 0.015 0.005 0.025 0.015 0.005 0.030 0.020 0.010 0.000 0.030 0.020 0.010 0.000 0.030 0.020 0.010 0.000 20 20 20 19 19 19 18 18 18 17 17 17 N=3 16 16 16 V magnitude 15 15 15 14 14 14 13 13 13 0.02 0.02 0.02 0.01 0.01 0.01 0.05 0.05 0.05 0.03 0.03 0.03 0.00 0.00 0.00 0.06 0.06 0.06 0.04 0.04 0.04 20 20 20 19 19 19 18 18 18 17 17 17 16 16 16 N>1 15 15 15 V magnitude 14 14 14 13 13 13 12 12 12 0.02 0.02 0.02 0.01 0.01 0.01 0.05 0.05 0.05 0.03 0.03 0.03 0.00 0.00 0.00 0.06 0.06 0.06 0.04 0.04 0.04 20 20 20 19 19 19 18 18 18 17 17 17 16 16 16 N=1 15 15 15 V magnitude 14 14 14 13 13 13 12 12 12 11 11 11

0.12 0.02 0.12 0.02 0.12 0.02 0.08 0.08 0.08 0.10 0.00 0.10 0.00 0.10 0.00 0.06 0.06 0.06 0.04 0.04 0.04

ro npooercindexes photometric in error

OLD NEW-B E- . NEW-A Figure 4.13: Photometric accuracygroups for of all stars. the indexes for the three catalogs (from top to bottom: OLD, NEW-A, NEW-B) for the four Part III

STELLAR PHYSICAL PARAMETERS

Chapter 5

Empirical calibrations

There are several pre-Hipparcos empirical calibrations that allow us to compute physical parameters from the Strömgren photometric indexes. There are three main steps that these procedures follow. First, to classify the stars in different photometric regions. Then, and depending on the region, they follow different calibrations to obtain both, the interstellar extinction and absolute magnitude, from which one can compute the distance. Finally, other parameters like Teff , log g, can be obtained from atmospheric model, and M/M and age from evolutionary models. Metallicity can also be obtained for some of the photometric regions. All these methods use as input the following reddening free photometric indexes:

[m1]=m1 +0.33 · (b − y) (5.1)

[c1]=c1 − 0.19 · (b − y)

[u − b]=[c1]+2· [m1]

Hβ = HβW − HβN and also the indexes: a =(b − y)+0.18 · ((u − b) − 1.36) (5.2)

r =0.35[c1] − Hβ +2.565 These empirical calibration methods (EC from now on) need first a photometric classification in different regions. Then two different parameters are computed: the interstellar extinction AV and the absolute magnitude MV . Each of the methods uses their own calibrations to derive these values. Most of them obtain the interstellar extinction from the intrinsic (b − y)0 color, and so from the excess. Crawford & Mandwewala (1976) provide useful relations between the excesses for different indexes as well as for the absolute absorption in the visible.

AV =4.27 · E(b − y) (5.3) E(a)=1.288 · E(b − y)

E(c1)=0.19 · E(b − y)

E(m1)=−0.33 · E(b − y)

Once the AV and MV are obtained, the distance can be computed as: − − Dist =10(5+V MV AV )/5 (5.4)

63 64 CHAPTER 5. EMPIRICAL CALIBRATIONS

In next sections, the methods used to derive the interstellar absorption and absolute magnitude for different classification regions are discussed, as well as the classification methods available. Then, in Sect.5.3 the computation methods for other physical parameters like Teff ,logg or Age are also described.

5.1 Classiﬁcation methods

Str¨omgren (1966) classiﬁed the stars in the following photometric regions:

• Early group (region 1): O-B9

• Intermediate group (region 2): A0 - A3

• Late group: Region 3: A3 - F0 Region 4: F0 - G2 Region 5: G2 –>

In our studies we are mainly interested in early regions, so the stars in regions later than 3 will not be taken into account. There are two references available that classify the stars in regions: Figueras et al. (1991) (FTJ91 from now on) and Lindroos (1980) (LI80). These methods use the reddening free photometric indexes [m1], [c1], [u − b], and Hβ to classify the stars in the different regions. In Fig.5.1 (left and center) we see the strategy followed by these two methods. As we can see they use slightly different indexes and relations in order to do the classification, FTJ91 being slightly more complex. Fig.5.2 (top and center) shows the resulting classification for the stars in our catalog. The two methods are very similar, with the main differences being in the gap between regions 1 and 3 in the [c1] − [m1] plot. They are equivalent when the stars in regions 1 and 3 are well separated (i.e. for small photometric errors). For the stars in our catalog this is not true, and the separation between early and late stars is not clear. In this case, the LI80 method has some problems with these stars, since they are classified as region 2 stars, when they should be region 1 or 3. So we can state that FTJ91 classifies better than LI80. However there are still some features in the FTJ91 classification that could be improved. First, there are some stars classified as region 1 with [m1] values larger than 0.16, that should be classified as regions 2 or 3 (see black points in Fig.5.2-top). On the other hand, the separation between early and late stars looks too sharp (see black and green points in Fig.5.2-top). The separation looks better in the LI80 classification, but just shifting the stars in the gap to later regions (instead to region 2 following LI80, or to region 1 following FTJ91). So a new classification method (NC from now on) is created here. It is based on the FTJ91 method, with two new modifications:

• A: The stars with [m1] > 0.16 cannot be region 1, so they will be reclassiﬁed as region 2 or later.

• B: We create a new separation between early and late regions using the LI80 separation and classifying the stars that LI80 was including in region 2 as region 3 or later. 5.1. CLASSIFICATION METHODS 65

We can see the NC scheme in Fig.5.1-right and the result of the classification in Fig.5.2-bottom. From now on, the method that will be used for classification is NC, rejecting the other two methods LI80 and FTJ91. 66 CHAPTER 5. EMPIRICAL CALIBRATIONS omgren (1966). Figure 5.1: Schemedifferences of between the methods. classification In for blue, reference FTJ91 tables (left), from Lindroos Str¨ (1980) (center) and NC (right). In orange and red we show the 5.2. EXTINCTION AND ABSOLUTE MAGNITUDE COMPUTATION 67

5.2 Extinction and absolute magnitude computation

This section details the diﬀerent calibrations available for each of the photometric regions that will allow the computation of the absolute magnitude MV and extinction AV . Then, through Eq.5.4 the distance will be computed.

5.2.1 Early region: O-B9 type stars

Crawford (1978) (CR78)

1. Assuming c0 = c1, the interpolation in Table I from Crawford (1978) provides a ﬁrst estimation for (b − y)0.

2. The excess is obtained E(b − y)=(b − y) − (b − y)0.

3. Using that value and Eq.5.3 we can obtain a new unreddened value c0 = c1 − E(c1)

4. Then the new value for c0 is used as input for the Table I again. The last steps are iterated until convergence obtaining a good value for AV .

5. From the same table one gets Hβzams.

6. Then Table V (Crawford 1978) provides MV (β) from the observed Hβ.

7. In some cases a correction to MV is applied:

MV = MV (β)ifc0 < 0.2

MV = MV (β) − 10 · (βzams − β)if0.2

MV = MV (β)ifc0 > 0.9

Lindroos (1981) (LI81)

• This method follows the same procedure as CR78, but shortening the range of correction of MV :

MV = MV (β)ifc0 < 0.2

MV = MV (β) − 10 · (βzams − β)if0.2

MV = MV (β)ifc0 > 0.75

This correction was computed using only 11 stars.

Balona & Shobbrook (1984) (BS84)

The steps followed to get c0 and E(b−y) are the same as in CR78. Then, the absolute magnitude is computed as:

• [g]=log(β − 2.515) − 1.60 · log(c0 +0.322).

3 • MV =3.499 + 7.203 · log(β − 2.515) − 2.319 · [g]+2.938 · [g] . 68 CHAPTER 5. EMPIRICAL CALIBRATIONS

Figure 5.2: [c1] − [m1] diagram where the colors show the region following FJT91 (top), LI80 (center) and NC (bottom). Black: region 1. Blue: region 2. green: region 3. Yellow: region 4. Red: region 5. 5.2. EXTINCTION AND ABSOLUTE MAGNITUDE COMPUTATION 69

5.2.2 Intermediate regions: A0-A3 type stars

Claria Olmedo (1974)(CL74)

• In this case the extinction is computed as: E(b − y)=0.692(b − y) − 1.073 · m1 − 0.065 · c1 +0.523 · Hβ − 1.265

• And from that the excess in a, and the unredden a0 = a − E(a).

• the absolute magnitude then is computed like: MV =1.5+6·a0 −17·r (Str¨omgren (1966))

Grosbol (1978) (GR78)

• The intrinsic a0 index and (b − y)0 color are computed like:

a0 =1.538 · [m1]+0.742 · r − 0.271

(b − y)0 =1.071 · [m1]+0.387 · r − 0.189

• So two diﬀerent excesses can be computed:

E(b − y)1 =(a − a0)/1.288

E(b − y)2 =(b − y) − (b − y)0

• The ﬁnal excess is computed from the average: E(b − y)=(E(b − y)1 − E(b − y)2)/2

• and then the absolute magnitude MV is obtained from Str¨omgren (1966):

MV =1.5+6· a0 − 17 · r

Hilditch et al. (1983) (HI83)

• Assuming m0 = m1, the interpolation in their Table 1 provides (b − y)0.

• The excess E(b − y) is computed, as well as the unreddened index m0 = m1 − E(m1).

• Using this new m0 in the table 1 again, and repeating last steps until convergence.

• MV is computed following GR78.

Moon & Dworetsky (1985) (MO85)

• Intrinsic color in computed as: 2 (b − y)0 =4.2608 · [m1] − 0.5392 · [m1] − 0.0235

• That provides excess and intrinsic index m0 = m1 − E(m1)

• m0 is used as input for Table 1 from Hilditch et al. (1983) to get (b − y)0 again.

• with the new value of (b−y)0, m0 can be recomputed, repeating the steps until convergence.

• For MV ,thestepsarethesameasfortheHI83method. 70 CHAPTER 5. EMPIRICAL CALIBRATIONS

5.2.3 Late region: A4-A9 type stars.

Crawford (1979) (CR79)

• Hβ is used as input in Table 1 from Crawford (1979) to get the non-evolved intrinsic indexes c0 and m0. MVzams is also computed.

• The diﬀerences are computed following:

δm1 = m0 − m1, that will be used as metallicity parameter.

δc1 = c1 − c0, that will be used as evolutionary parameter.

• The intrinsic color (b − y)0 is computed following two diﬀerent formulas, as a function of the δm1.

(b − y)0 =2.946 − Hβ -0.1δc1 if δm1 >0

(b − y)0 =2.946 − Hβ − 0.1δc1 − 0.25δm1 if δm1 < 0

• With that we obtain the excesses in the diﬀerent indexes as well as the unreddened indexes m0 and c0.

• And then δc1 and δm1 are recomputed, iterating until convergence.

• The absolute magnitude is obtained from MV = MVzams− 9 · δc1.

5.3 Eﬀective temperature and other physical parameters

Using previous methods we obtained the interstellar extinction and the absolute magnitude (thus the distances) for all the photometric regions. But parameters like luminosity, age, Teff , log g or Mass are still not available. In order to obtain all these parameters, atmosphere models and stellar evolutionary models can be used (as it will be done for the Model Based method, see Chapter 6). Using the obtained intrinsic color indexes (b−y)0, m0, c0 and Hβ we can interpolate in the atmospheric grids in order to obtain the Teff and log g, as well as the bolometric correction. The luminosity can be obtained from the absolute magnitude and the bolometric correction: Mbol = MV + BC and log(L/L)=(−Mbol +4.74)/2.5. And then, the Teff and L/L can be used to interpolate in the evolutionary track to obtain the age and the Mass. Metallicity is diﬃcult to be computed and for most of the regions there is no available metallicity calibrations. For region 3 stars there are calibrations that compute it from the δm1 index, like those provided by Smalley (1993):

[H/M]=−10.56 · δm0 +0.081 (5.5) or by Berthet (1990):

− · 2 − [Fe/H]= 35.139 δm0 6.515δm0 +0.081 (5.6)

For later regions (F stars and colder) there are other calibrations available like Crawford (1975); Nissen (1970, 1988); Gustafsson & Nissen (1972); Crawford & Perry (1976). However, we are not interested in cold stars, so these methods are detailed here. 5.4. ERROR COMPUTATION 71

5.4 Error computation

In order to provide errors for the obtained physical parameters there are two main options. The first one is to follow the formulas provided by Reis & Corradi (2008) (for B-type stars) and Knude (1978) (for A-type stars). These formulas are obtained from the error propagation in the previous empirical relations. The other option (that will be used in this work) is to compute the errors through Montecarlo simulations, that is, to use the original error in the observed photometric indexes (V ,(b − y), m1, c1,andHβ) to create several random realizations. We will assume Gaussian distributions for the errors to obtain the final dispersion for each of the physical parameters. This method allows to compute all the errors following the same approach for all the photometric regions. It will be also directly comparable with the errors we will use for the Model Based method (see Chapter 6). 100 realizations will be used in both cases in order to estimate the errors for the different physical parameters. The 100 random realizations developed can be classified in different photometric regions, and so the physical parameters will be computed using different procedures (or will not be computed for stars in region 4 or 5). So in order to homogenize the results, a given realization will only be used to compute the error if it is located at the same region as the original star (the one coming from the catalog without any random modification). And in order to understand where the different realizations are classified, and how many of them are used for the final error computation, we are keeping track of the number of realizations for each of the regions through the parameter Nreg. We must take into account that the photometric errors provided by the catalog are the error of the mean for stars with more than one measure. In that case, the output error will be also the error of the mean. But for stars with a single photometric measurement, the error provided by the catalog is just the dispersion obtained by error propagation from all the process, so the output errors for the parameters will be coherent with that. 72 CHAPTER 5. EMPIRICAL CALIBRATIONS Chapter 6

The new strategy: Model Based method

We created a second method to obtain physical parameters from Strömgren photometric indexes based on atmospheric and evolutionary star models (Model Based method, MB from now on). It consists in a two step approach. First, a 3D fit in a [c1] − [m1] − Hβ grid that provides gravity (log g), effective temperature (Teff ), intrinsic color ((b − y)0 -from which we can get the absorption (AV )- and the bolometric correction (BC). And second, the interpolation in an evolutionary track that provides luminosity (L/L) and age. This luminosity is translated into bolometric magnitude using: L Mbol =4.74 − 2.5log (6.1) L And using the bolometric correction, the absolute magnitude in the V band can be computed like: MV = Mbol − BC (6.2)

And then the distance is computed using Eq.5.4 from MV , AV and the observed V magnitude. This section details all the steps followed for the method, the diﬀerent available grids are presented and discussed.

6.1 Model atmospheres

Atmospheric grids are needed, providing the corresponding Strömgren photometry for different kind of stars. F.Castelli provides in her webpage1 the colors for different photometric systems obtained from ATLAS9 atmospheric models (Castelli & Kurucz 2006, 2004). Each grid contains:

• eﬀective temperature (Teff ), • gravity (log g),

• Str¨omgren unreddened indexes ((b − y), m1, c1, Hβ), and • bolometric correction (BC).

1http://wwwuser.oat.ts.astro.it/castelli/colors.html

73 74 CHAPTER 6. THE NEW STRATEGY: MODEL BASED METHOD

Table 6.1: Information for the diﬀerent grids grid uvby Hβ convection Teff range log g range Castelli yes yes MLT 3500 - 50000 0-5.0 Smalley 1997 yes no MLT 5500 - 8500 2-5.0 Smalley 1995 no yes Turbulent (CM) 5500 - 50000 0-5.0

In addition to the grids provided by Castelli, Smalley & Dworetsky (1995); Smalley & Kupka (1997) provide grids only available for later stars. The main diﬀerence between Castelli and Smalley & Kupka (1997) grids are the convection models used. While Castelli is using the mixing length theory (MLT), Smalley & Kupka (1997) is using the turbulent convection model from Canuto & Mazzitelli (1991, 1992) (CM from now on). However, Smalley & Kupka (1997) do not provide the Hβ values, that can be obtained from Castelli grids or from Smalley & Dworetsky (1995), that used Kurucz (1979) grids as well as MLT. Table 6.1 provides information about the diﬀerent available grids. Some important comments and statements from the papers:

• Convecting models (CM) theory gives values of (b − y)0 and c0 that are in best overall agreement with observations. Investigations of the m0 index reveal that all of the treat- ments of convection presented (Smalley & Kupka 1997) gives values that are signiﬁcantly discrepant for models with Teff <6000K. None of the models give totally satisfactory m0 indexes for hotter stars, but CM models are in good agreement above 7000K.

• Broad band colors and flux distributions are significantly influenced by microscopic effect of convection in stars later than mid A-type.

• Small systematic errors were found (in Kurucz 1979, ATLAS6) in the colors calculated for late-A and F stars.

• For early-A type stars there is a region around the zone of hydrogen ionization that is convectively unstable according to the Schwarzschild criterion, but convective transport remains so ineﬃcient that the resulting temperature gradient cannot be distinguished from the radiative one. In the case of MLT, minor deviations from the radiative gradient can be observed beginning around Teff =8500K,logg=4.

In Fig.6.1 and 6.2 we see the differences between the grids. In Chapter 7 we will compare the results obtained using different atmospheric grids with Hipparcos data in order to check which is the best grid (or combination of grids) for the distance derivation. Figure 6.3 shows the differences between the photometric indexes provided by the Castelli and Smalley & Kupka (1997) grids. And in Fig. 6.4 there are the differences in Hβ between Castelli and Smalley & Dworetsky (1995). Some comments about the plotted differences are:

• The diﬀerences in (b − y)0 are always positive, i.e. (b − y)0 from Castelli are larger. Diﬀerences are up to 0.025.

• The largest diﬀerences are given for c1. Castelli values for cold stars are clearly larger (up to 0.06). The diﬀerences are smaller (only up to 0.02) for hotter stars. 6.1. MODEL ATMOSPHERES 75

1.8

8000 1.6 7500 8500

1.4 7000

1.2 6500 1 c1 6000 0.8

0.6 5500 2.0 2.5 0.4 3.0 3.5 4.0 4.5 0.2 5.0 0 0.1 0.2 0.3 0.4 0.5 (b-y)0

Figure 6.1: Comparison of the (b − y)0 and c1 for the Castelli (blue) and Smalley (green) grids.

0.35

0.3 5500

0.25 5.0 m1 4.5 6000 0.2 4.0

3.5 6500 7000 0.15 3.0 7500

2.5 8000 2.0 0.1 8500 0 0.1 0.2 0.3 0.4 0.5 (b-y)0

Figure 6.2: Comparison of the (b − y)0 and m1 for the Castelli (blue) and Smalley (green) grids. 76 CHAPTER 6. THE NEW STRATEGY: MODEL BASED METHOD

Figure 6.3: Diﬀerences (Castelli - Smalley97) in (b − y) (left), m1 (center) and c1 (right) as a function of Teff (top) and log g (bottom). Solid lines show log g=2.0 (red), log g=3.0 (blue), log g=4.0 (green) and log g=5.0 (orange). Dashed lines show diﬀerences for Teff =5500 (red), Teff =6500 (blue), Teff =7500 (green) and Teff =8500K (orange)

• Diﬀerences in m1 are small for low gravities and low Teff , but then they increase up to 0.03 for log g=4.5-5. Castelli values are slightly larger for cold stars and clearly smaller for large gravities.

• The diﬀerences reach 0.03 magnitudes for Teff ∼8000 K.

• For stars hotter than 10000 K the diﬀerences are insigniﬁcant.

• Since our region 3 stars have Teff =7000-8500 K we have stars with both, positive and negative diﬀerences.

6.2 Interpolation method

The different grids provided by Castelli & Kurucz (2006), Smalley & Dworetsky (1995) and Smalley & Kupka (1997) are discretized in steps of 0.5 or 0.25 in log g and 250K, 500K,or 1000K in Teff (depending on the grid and the range of Teff ). Since we will develop a 3D fit we need to discretize the grids as much as possible, taking into account the final accuracy in physical parameters and also the computing time. The appropriate steps for the interpolated grids have found to be 10 K in Teff and0.01inlogg. There are two possible interpolation methods that can be used here, namely a linear interpolation between the available points or a smoothed interpolation using a gaussian weighted mean with all the points around it. Each of the options has its drawbacks. In the case of the linear 6.3. STELLAR EVOLUTIONARY TRACKS 77

0.04 0.03

0.03 0.02 0.02 0.01 0.01 DHb DHb 0 0

-0.01 -0.01

-0.02 -0.02 6000 7000 8000 12345 Teff logg

Figure 6.4: Differences (Castelli - Smalley94) in Hβ as a function of Teff (left) and log g (right). Solid lines show log g=2.0 (red), log g=3.0 (blue), log g=4.0 (green) and log g=4.5 (orange). Dashed lines show differences for Teff =5500K (red), Teff =6500K (blue), Teff =7500K (green) and Teff =8500K (orange). interpolation, we ensure that the thin grid goes exactly through the original grid, but some sharp features are created that, mainly at the turning point of the grid (at the upper part of the [c1] − [m1] − Hβ diagram, close to intermediate region), will cause a different probability for a star to belong to each of the points. The stars above the grid will have more probabilities to be fitted with the points at the edges of the sharp features. That fact creates some discontinuities to our final results. On the other hand, for the smooth interpolation, the main drawback is that the final points will not match with the original points of the grids. Depending on the sigma used for the smoothing, the differences between the original and the thin grid can be important, mainly at the top of the grid. In addition, the results depend on the sigma used and on the discretization of the original grid, so we find some discontinuities when the step size of the original grid changes.

For all these regions we decided to use a smoothed interpolation for points below Teff <12000 K, that includes the peak around intermediate region and also the transition between Castelli & Kurucz (2006) and Smalley & Dworetsky (1995) grids, avoiding sharp features. And then, to use a linear interpolation for the hotter grids, where the original grid has a different step size, avoiding discontinuities. In any case, the differences between different options are always below 0.005 for [c1], 0.002 for [m1] and 0.003 for Hβ. And the differences in the final distances obtained using the two grids are around 2% in distance.

6.3 Stellar evolutionary tracks

There are two evolutionary tracks available in the literature useful for our purposes: Bressan et al. (1993) and Bertelli et al. (2008). Bressan et al. (1993) provide 20 grids within a range of Masses between 0.6 -120M.Thelogg is not provided, but it can be computed from the Mass, the luminosity and the Teff taking into account the expressions 6.3 and 6.4 that can be 78 CHAPTER 6. THE NEW STRATEGY: MODEL BASED METHOD obtained from:

L =4πR2σT 4 eff 2 1 −4 R = L Teff 4πσ 1 2logR =log +log(L) − 4log(Teff ) 4πσ 1 L 2logR =log +log +log(L) − 4log(Teff ) 4πσ L and using (in cgs units): 1 σ =5.6704 · 10−5erg · cm−2s−1K−4 log =3.147176 4πσ 33 −1 L =3.839 · 10 erg log L =33.584218 we get the expression L 2logR =3.147176 + 33.584218 + log − 4logTeff (6.3) L On the other hand: M g = G R2 − log g =logG +logM 2log R M log g =logG + log +logM − 2logR M and using (in cgs units):

G =6.67428 · 10−8cm2 · g · s−2 log G = −7.175596 33 M =1.9891 · 10 glogM =33.29866 we get the expression: M log g = −7.175596 + 33.29886 + log − 2logR (6.4) M

Bertelli et al. (2008) provide 32 tracks with masses between 0.6 and 20 M. Stars more massive than that are not important in this study (a 20M isaO8starwhileaB0has17.5M). The grids for more massive stars can be obtained from Bressan evolutionary tracks, and although they do not provide the Mass loss, they provide log g, so the Mass can be computed inverting Eqs. 6.3 and 6.4. From all the metallicity grids provided, the solar metallicity grid is used: Z=0.017, Y=0.26 (Grevesse & Sauval 1998). Figure 6.5 compares both evolutionary tracks. And Figs.6.6 and 6.7 show the comparison between the resulting physical parameters for our anticenter survey stars using the two diﬀerent 6.4. THE ROLE OF METALLICITIES 79

M=20Mo

4.4

M=5Mo 4.2

4 log Teff

3.8 M=1Mo

3.6 M=0.6Mo

3.4 012345 log g

Figure 6.5: log g vs. log Teff for the Bressan (red) and Bertelli (blue) grids. Four different masses are shown as an example. grids. There are around ∼1% of stars that have problems and which distances cannot be computed following this method, since they are outside the grids. As can be seen in Fig.6.7, the differences between the two grids are small, leading to differences in distances smaller than 5%. The differences are also smaller than 0.2 in absolute magnitude and 0.06 in luminosity. Since the discrepancies are small, the Bertelli et al. (2008) tracks will be selected because they are more recent.

6.4 The role of metallicities

AccordingtoNordström et al. (2004), the metallicity in the solar neighbourhood is slightly negative, with a mean value of [M/H]=-0.14±0.19 dex. Grevesse & Sauval (1998) suggest values of Z=0.017, Y=0.26 from the study of the Sun. On the other hand, the gradient of metallicity as a function of the Galactic radius has been found to be around 0.1dex/kpc. The stars we are interested in will be not further than 3-4 kpc, so their mean metallicities will lay in the range between [M/H]=[-0.5,0.0]. Our fitting method do not allow to compute metallicity at the same moment that we obtain other parameters like Teff and log g, due to the large degeneracy present in the 3D space [m1] − [c1] − Hβ. So, although different metallicity grids are available, solar metallicity grid will always be used. However, we develop some tests in order to check the biases that are introduced when solar metalicity grid is assumed, and compare them with a grid with [M/H]=-0.5. Figure 6.8 present the differences between the Castelli grids with [M/H]=0.0 and [M/H]=-0.5. The differences increase up to 0.4-0.5 dex for cold stars, but for the hotter stars we are intereseted in (e.g. Teff >7000K,log(Teff ) =3.85, for a A9 star), the differences in [m1]and[c1] are smaller 80 CHAPTER 6. THE NEW STRATEGY: MODEL BASED METHOD

Figure 6.6: log g vs. Teff with the luminosity, Age and MV color-plotted. Left: using Bressan et al. (1993) grids. Right: Using Bertelli et al. (2008) grids. The jump in Age around the main sequence is due to all the stars below the zams, since they are shifted to the zero age. 6.4. THE ROLE OF METALLICITIES 81

Figure 6.7: Differences between the physical parameters obtained using Bressan et al. (1993) and Bertelli et al. (2008) tracks. From top to bottom: Differences in distance (in pc), luminosity, absolute magnitude and age. Left: Histogram of the mentioned differences. Right: Differences vs. distance, luminosity, absolute magnitude and age. 82 CHAPTER 6. THE NEW STRATEGY: MODEL BASED METHOD

0.02 0.020

0.06 0.015 0.00 0.010

5 0.04 . 5 0 . 5

. 0.005 0 − 0

] −0.02 − − ] 1 1 m c [ [ Hb 0.000 − − − 0 0 0 . . 0.02 . 0 0 0 ] ] −0.04 1 1 −0.005 c Hb [ m [ −0.010 0.00 −0.06 −0.015

−0.02 −0.08 −0.020 3.6 3.8 4.0 4.2 4.4 4.6 3.6 3.8 4.0 4.2 4.4 4.6 3.6 3.8 4.0 4.2 4.4 4.6

log(Teff) log(Teff) log(Teff)

Figure 6.8: Diﬀerences in [m1], [c1]andHβ as a function of Teff for two diﬀerent Castelli metallicity grids, with [M/H]=0.0 and [M/H]=-0.5,

Figure 6.9: [c1] − [m1] plots where colors show the differences in Teff ,logg and distance (in pc) when comparing two different Castelli metallicity grids, with [M/H]=0.0 and [M/H]=-0.5. than 0.02 mag and the differences in Hβ are smaller than 0.01. These values are below our photometric errors and although they can lead to small systematic trends, the differences are very small for the final physical parameters. As can be seen in Fig.6.9, there are only two regions with larger biases: the cold stars and the gap between early and late type stars, where the stars can have missclassification problems. Figure 6.9 shows the differences in Teff and log g and final distance obtained when using the two different metallicity grids. As stated, the differences are very small, except for two regions: the gap between early and late regions, where some stars may be different classified, and the late type stars.

As known, [m1] is a good Str¨omgren indicator of metallicity for stars later than A3 (with log(Teff ) <3.9), so it should be possible to use this parameter o estimate the metallicity for some of our catalog stars.

6.5 Binarity eﬀect

Many of the stars in our survey will be binaries. Some of them will be just visual binaries while others will be real physical binaries. In the first case, it is very difficult to estimate their effect, since the ratio between their masses, distances, spectral types, etc. can be any. However only the pairs with similar brightness will be really important for us. For physical binaries, some tests can be developed in order to estimate the change in their photometric indexes. The ratio of binarity is under discussion, but according to Arenou (2010) it can reach more than 80% for the more massive stars. There are several parameters that will be important when studying the 6.5. BINARITY EFFECT 83 modification of the photometry due to a binary star, some of them being:

• Probability of binarity: according to Arenou (2010) this probability can reach 80% for most massive stars.

• Mass ratio between the stars (M1/M2): It is related with the ratio of the magnitudes, and so the eﬀect of the secondary on the photometry of the primary. According to Arenou (2010) the probability have a peak around M1/M2=0.6. And only in 10% of the cases the mass ratio is higher than M1/M2=0.8.

• Period and radius of the orbit: together with the distance and angular resolution, they give the limit for the detection of the two stars.

• Inclination angle of the orbit: that will give probability of eclipsing binaries.

The simulation of all these effects can be very complex. In order to have a first estimation, a simple simulation is developed here, analysing the change on the photometric indexes for different mass ratios. The steps followed in this simulation are:

1. Select diﬀerent main sequence type stars as example of the primaries, from B0 to F0.

2. Obtain the typical physical parameters for these primary stars: absolute magnitude MV 1, Mass M1 and temperature Teff1.

3. Assume, for each primary, diﬀerent type stars for the secondary (always with less mass than the primary), as well as their physical parameters: absolute magnitude MV 2,Mass M2 and temperature Teff2.

4. Assume that all the stars are main sequence with a gravity of log g =4.2.

5. For each star (both, primaries and secondaries) obtain their photometric indexes ((b − y), m1, c1, Hβ) from the Castelli & Kurucz (2004) grids and the assumed Teff and log g.

6. Assume a V magnitude for all the stars. We will assume that the distance is 10pc, and there is no extinction, so the visual magnitude will be V = MV . The results do not depend on this assumption.

7. Compute the magnitudes in the individual ﬁlters from the given photometric indexes like: y = V , b =(b − y) − V , v = m1+2(b − y)+V , u = c1 +2m1 +3(b − y)+V , HβW = b, and HβN = Hβ− HβW . We are assuming that b and HβW are approximately equal since they are centered at similar wavelengths.

(−x/2.5) 8. Compute the individual ﬂuxes for each star Fx =10 +C for x = u, v, b, y, HβW ,HβN .

9. Obtain the total flux for each filter adding the fluxes for both stars: FxT = Fx1 + Fx2.

10. Obtain the total magnitudes in the individual ﬁlters: xT = −2.5log(FxT ).

11. Compute the ﬁnal index for the binaries like: (b − y)T = bT − yT , m1T = vT − 2 · bT + yT , c1T = uT − 2 · vT + bT and HβT = HβNT − HβWT. 84 CHAPTER 6. THE NEW STRATEGY: MODEL BASED METHOD

1.2 K5 3.0 K5 K2 K2 1.0 K0 K0 G8 2.9 G8 G5 G5 0.8 G2 G2 G0 G0 2.8 0.6 F5 F5 ] 1 1

1 F2 F2 c Hb [ 0.4 F0 SP F0 SP 2.7 A5 A5 A2 A2 0.2 A0 A0 B8 2.6 B8 0.0 B5 B5 B2 B2 −0.2 B0 2.5 B0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.0 0.1 0.2 0.3 0.4 0.5 0.6

[m1 ] [m1 ] 1.2 1.0 3.0 1.0

0.9 0.9 1.0 0.8 2.9 0.8

0.8 0.7 0.7 1 1 0.6 2.8 0.6 0.6 ]

1 0.5 0.5 /Mass /Mass c Hb [ 0.4 2 2 0.4 2.7 0.4 Mass Mass 0.2 0.3 0.3 0.2 2.6 0.2 0.0 0.1 0.1

−0.2 0.0 2.5 0.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.0 0.1 0.2 0.3 0.4 0.5 0.6

[m1 ] [m1 ]

Figure 6.10: Displacement due to binarity in [c1] − [m1](left)andHβ − [m1] (right) plots. Crosses show the location of the primary, and dots the location of the total binary star. Top: colors show the spectral types of the binary for each simulated star. Bottom: colors show the mass ratio between the primary and the secondary.

The information about the spectral types used, and their physical parameters as well as the photometric indexes can be found in Table A.11. In Fig. 6.10 and Fig. 6.11 we can see how the indexes [m1], [c1]andHβ have been modiﬁed due to the presence of the secondary star. We see that for diﬀerent Teff of the primaries and for some mass ratios between the primary and the secondary the photometric indexes can be shifted up to 0.1. For hot stars, only mass ratios very close to one gives biases close to 0.05 in [c1], up to 0.2 in [m1] and up to 0.04 in Hβ.Theseare upper limit values, since these combination of stars will be found in few cases.

Finally, it is important also the effect on absolute magnitude MV . Considering two stars with equal luminosity, that have been treated as a single star, this translate in an error of absolute magnitude of 0.75mag (i.e. for a single star: m1 = −2.5logF1 + C, but if the star is binary: F2 =2F1,andthenm2 = −2.5log(2F1)=m1 − 0.75). This error of 0.75 magnitudes is translated into a 30% error in distance for this extreme case. The mass ratio between the primary and the secondary is a critical issue for the MV derivation of the star (or system). As stated, only 10% of the OB stars have mass ratio larger than M1/M2=0.8 (Arenou (2010)). So very few stars will be close to this extreme case of a 0.75 magnitude error. This possible bias in the MV determination will lead to a direct shift in the position of the arm. The only solution available to correct this effect is the spectroscopic analysis of the stars in order to remove those that are clearly binaries. We are only considering main sequence stars. In the case of evolved stars, we have to take into account that star evolution will affect more the primary (more massive star) shifting it out of the main sequence and giving a brighter magnitude. In that case, since the primary will be brighter, the effect in the final photometry will be even smaller. 6.6. 3D FITTING ALGORITHM 85

0.10 0.10 1.0

32000 0.9

0.8 28000 0.05 0.05 0.7

24000 1

1 1 0.6 ] ] 1 1 c c 1 [ 0.00 20000 [ 0.00 0.5 /Mass − − eff 2 T T T ] ] 1 1

c c 0.4

[ 16000 [ Mass 0.3 −0.05 12000 −0.05 0.2 8000 0.1

−0.10 4000 −0.10 0.0 −0.01 0.00 0.01 0.02 0.03 0.04 0.05 −0.01 0.00 0.01 0.02 0.03 0.04 0.05

[m1 ]T −[m1 ]1 [m1 ]T −[m1 ]1 0.06 0.06 1.0

32000 0.9 0.04 0.04 0.8 28000 0.7 0.02 0.02

24000 1 0.6 1 1 1 Hb 0.00 20000 Hb 0.00 0.5 /Mass − − eff 2 T T T 0.4 Hb 16000 Hb

−0.02 −0.02 Mass 0.3 12000 0.2 −0.04 −0.04 8000 0.1

−0.06 4000 −0.06 0.0 −0.01 0.00 0.01 0.02 0.03 0.04 0.05 −0.01 0.00 0.01 0.02 0.03 0.04 0.05

[m1 ]T −[m1 ]1 [m1 ]T −[m1 ]1

Figure 6.11: Diﬀerences in [c1], [m1]andHβ between the primary and the binary star. Left: color shows the Teff of the primary. Right: color shows the mass ratio between the primary and the secondary.

6.6 3D ﬁtting algorithm

The photometric indexes from our catalogued star need to be fitted with the atmospheric grids, in order to find which is the point of the grid that best represents the star. Four different methods are defined to compute the Teff ,logg,(b − y)0 and BC from the observed photometric indexes and their errors using the atmosphere grids described in Sect.6.1.

6.6.1 Method 1: Gaussian weighted mean

For each star, the Teff and log g are computed as the average for all the points of the grid (i), weighted with a gaussian as a function of the distance between the position of the star and the point of the grid, that is: −([c1] − [c1] )2 −([m1] − [m1] )2 −(Hβ − Hβ )2 T = W T exp i − i − i eff effi 2σ2 2σ2 2σ2 i [c1] [m1] Hβ −([c1] − [c1] )2 −([m1] − [m1] )2 −(Hβ − Hβ )2 log g = W log g exp i − i − i i 2σ2 2σ2 2σ2 i [c1] [m1] Hβ where (6.5) 1 −([c1] − [c1] )2 −([m1] − [m1] )2 −(Hβ − Hβ )2 = exp i − i − i (6.6) W 2σ2 2σ2 2σ2 i [c1] [m1] Hβ 86 CHAPTER 6. THE NEW STRATEGY: MODEL BASED METHOD

The main drawback of this method is that for stars in the gap between region 1 and 3 (stars with [m1] ∼0.2) the result is the average between physical parameters from both sides. One should assign the star to one of the sides (early or late-type stars), but the average of the properties of the early and late-type stars will give some result that has no physical sense.

6.6.2 Method 2: Minimum distance

This second method looks for the point of the grid that is closer to our star. To do that we created a thin grid interpolating the original one (see Sect. 6.2.) The distance between the star () and a point of the grid (i) is computed as: − 2 2 − 2 2 − 2 2 ([c1] [c1]i) ω[c1] +([m1] [m1]i) ω[m1] +(Hβ Hβi) ωHβ disti = 2 2 2 (6.7) ω[c1] + ω[m1] + ωHβ

1 with ωj = 2 , where the photometric error for each index is taken into account. The physical σj parameters are assigned to the star, according to the point of the grid that has the minimum distance to the star. Minimizing the distances is equivalent to maximize the probability. But following Eq.6.7, we are considering that the probabilities in each of these three axis are independent although they are not. Next method will take that into account.

6.6.3 Method 3: Maximum probability

This method maximizes the probability for one star to belong to a point of the grid, taking into account the distance between them (Dsg), as well as the photometric errors in the three indexes, that form the so-called ellipsoid of errors. The distance Dsg between the star (s)andthepoint of the grid (g) can be computed like:

2 2 2 − Dsg = Dsg,x + Dsg,y + Dsg,z = ξ ξg (6.8)

with Dsg,x =[c1]s − [c1]g, Dsg,y =[m1]s − [m1]g,andDsg,z =[Hβ]s − [Hβ]g being the distances in each of the axis, and ξ being the variable in the axis between the star and the point of the grid with the origin located at the star. And considering the ellipsoid of errors, the photometric error in the direction between the star and the point of the grid can be computed like the distance between the location of the star and the surface of the ellipsoid in the direction between the star and the point (see Fig.6.12). In some cases the photometric errors can be underestimated, giving probabilities too close to zero. So we will increase the size of the ellipsoid ﬁve times. Then the three axis of the ellipsoids are:

a =5σc1 b =5σm1 c =5σHβ

Then the distance between the star and the surface of the ellipsoid in each axis, computed from 6.6. 3D FITTING ALGORITHM 87

Figure 6.12: Scheme of the ellipsoid of errors that show how to compute the σsg between the star and any point of the grid from the individual errors of the three photometric indexes.

Figure 6.13: Scheme of the probability parameter. the equation of the ellipsoid and the equation of a line from the star to the point of the grid, is: D2 D2 D2 1 1 1 · sg,y 1 · sg,z · sg,y 2 = 2 + 2 2 + 2 2 2 1+ 2 Dse,x a b Dsg,x c Dsg,x + Dsg,y Dsg,x D2 2 sg,y · 2 Dse,y = 2 Dse,x Dsg,x D2 + D2 2 2 · se,x se,y Dse,z = Dsg,z 2 2 Dsg,x + Dsg,y An ﬁnally the distance between the star and the ellipsoid in the given direction is:

2 2 2 Dse = Dse,x + Dse,y + Dse,z (6.9)

Once we have these values, we can compute the probability for one star to belong to a point of the grid as a gaussian with sigma being Dse and centered at the star (see Fig.6.13):

∞ 1 ξg (ξ − ξ )2 (ξ − ξ )2 P =1− √ exp g dξ − exp g dξ (6.10) 2 2 Dse 2π −∞ 2Dse ξg 2Dse

Given one star, we have to compute the probability P for all the points of the grid in order to ﬁnd the point of the grid that gives larger probability Pmax. When the parameter P =0.32 88 CHAPTER 6. THE NEW STRATEGY: MODEL BASED METHOD

Figure 6.14: [c1]-[m1]anda[c1]-Hβ diagram with all the points of the grid. The color shows the corresponding probability P for an example star.

means that the point of the grid is located at 1Dse,andP =0.05 the grid will be at 2Dse.In Fig.6.14 we see, for a single star, the probability for all the points of the grid in a [c1]-[m1]and a[c1]-Hβ diagrams. It must be taken into account that stars in the gap between early and late type stars can have a two peak distribution of probability, that is, they can belong to either one or the other side of the gap. Although we always choose the point of the grid with larger probability, we should consider those cases where the probability is similar for two different points of the grid, one for early region stars and the other one for late region stars. In that case, we should keep track of the results for both, and decide afterwards, using other information, like the results obtained by Crawford or photometry from IPHAS, 2MASS, etc., which should be the final choice. In order to keep track of this second possible location of the star we computed a second probability (B) parameter Pmax that will be forced to be at the other side of the gap. The limit between the two sides is fixed at Teff =10000K. If the relation between the two probabilities Pmax and (B) Pmax is close to one, we would have a star with similar probabilities to belong to early and late regions. For intermediate stars (stars around A0), this limit have not much sense, since they lay at the peak of the distribution. We can consider that for the stars with [c1] > 0.85 this second probability parameter will not be important. The physical parameters obtained considering that the star should belong at the other side of the gap will be named as case B, so they will have a B subindex (e.g. Teff,B,loggB,etc.)

6.6.4 Method 4: Weighted maximum probability

This method is an improvement of method three to be applied to the stars that have similar probability to belong to both sides of the grid. We describe and discuss its advantages and drawbacks, but it will not be implemented in following sections. The maximum probability method (see Sect.6.6.3) assign Teff and log g taking into account both, the position in the [m1] − [c1] − Hβ and the corresponding photometric errors. As shown in Sect.4.4.2 the faint 6.6. 3D FITTING ALGORITHM 89 stars in our catalog have large photometric errors. This issue place some stars in the gap between early and late region (see Fig.5.2). Method 3 gives to these stars similar probabilities to belong to each of the two regions. To deal with this ambiguity some additional criteria are suggested here, each of them with its own advantages and disadvantages. These criteria could be, e.g.:

• From the luminosity function in the solar neighbourhood one would expect more stars in the late region than in the early region. One option could be to weight each point of the atmospheric grid according to the corresponding Hess diagram. This diagram has the advantage to give a weight as a function of Teff and log g. However, our observed sample is not volume complete, so it does not follow the distribution presented by this Hess diagram.

• A second approach would be to use a simulated sample from the Besan¸con Galaxy model for all the stars up to a given apparent magnitude in the anticenter direction. This approach is highly model dependent, so it can introduce some non-desired systematic trends (e.g. BGM has no spiral arms).

• The set of stars of our sample from which the assignation is clear using method 3 (Pmax) deﬁne a density distribution along the grid. This density can be used as a weight for each of the point grid. Following this procedure we have the advantage to really represent our working sample and not a previous known luminosity function.

A critical issue in the application of all these criteria is that any of the simulated samples would require a photometric error distribution similar to our working sample. The third criteria (using the correctly assigned stars) does not have this drawback, so it is the best one. We need to define for this method two samples. First the stars that we know for sure that are well assigned. We can select them by imposing a high probability Pmax >80% and also a (B) relation between the two probabilities Pmax/Pmax >2 (so the absolute maximum probability is larger than twice the maximum probability at the other side of the gap). Around 20% of the stars (∼7000) follow this requirements. On the other hand we also have to fix which are the ambiguous stars, those that are in the ambiguous region. We propose to use again the relation between the parameters, and their (B) (B) differences are smaller than 10%, that is, Pmax >0.9Pmax, i.e. Pmax/Pmax <1.1. But some of these stars are region 2 stars, close to the turn off of the diagram, and there is no ambiguity for them. So we need to restrict the sample to those stars with [c1] <0.85. This sample of uncertain stars following these restrictions are just the 4% of the sample (∼ 1300 stars) Using these ∼7000 stars that are considered as well assigned, we have to compute a weight for each of the points of the grid. Then a uniform grid in Teff -log g is created. It cannot be used the original thin grid used for the fit since it is too thin and almost no stars would be in each bin. SowecanuseagridwithastepofΔTeff =250K and Δ log g=0.5. Then the method 3 fitting is developed with the well classified stars. The number of stars fitted to each of the points of the grid, normalized by the total number of stars, is used as the weight assigned to each point. One drawback is that for lower gravities, there are almost no stars in each bin. And the weight appliedinlogg is not related with the two sides of the gap. So we can integrate for all the gravities, giving the weights only as a function of the temperatures. A second drawback for this method is with the upper part of the diagram, where the maximum probability parameters Pmax (B) and Pmax do not have much sense, since the assigned Teff will be close to 10000K in both cases, 90 CHAPTER 6. THE NEW STRATEGY: MODEL BASED METHOD

(B) (B) so Pmax/Pmax ∼ 1. To avoid that, they have been rejected by the restriction Pmax/Pmax >2. So there is a lack of stars in those bins, due to our selection but not due to the real luminosity function. So we should cut again at [c1] <0.85 and do not weight the points of the grid for intermediate region. All these drawbacks and extra criteria make the method really complex and with several possible bias. In addition, this method would have eﬀect only on 4% of the stars (those in the gap), so it will not be applied during this work, keeping the Method 3 as the onetobeused.

6.7 Error computation

The errors for the obtained physical parameters are estimated from Montecarlo simulations. 100 simulated stars are created for each of the stars in our sample, which value of the photometric indexes (V ,(b − y), m1, c1,andHβ) will be modified following a random Gaussian number using the photometric error as the sigma. Then we will obtain for each star, 100 values for the output physical parameters. The dispersion obtained for these 100 values will be used as the error for each physical parameter. Some of these realizations may be fitted at the other side of the gap of the original star. Then, the computed parameters will be really different, giving at the computed dispersion a large value with not really a physical sense. So the realizations will be used for the error computation, only when they are located at the same side of the gap than the original star (measure without adding any random error). This two sides are easy to distinguish for stars at the bottom of the diagram (with low [c1] value), but the limit between both sides is not so clear at the top of the sequence. So one realization will be selected for the error computation, only in these cases:

• When both, the original star and the realization have [c1] >0.85.

• When one of them or both have [c1] <0.85 and:

-BothhaveTeff <10000K,or

-BothhaveTeff >10000K.

Both the limit at [c1] =0.85 and Teff = 10000K have been set empirically in order to match with the turning point of the grids. That ensures that all the random realizations used for the error computation are at the same side of the gap, and the dispersion will be due to the error coming from the photometry and not for the difficulty of finding the right classification for the stars. However, this difficulty is also interesting to be checked, and that can be identified through an index Nside indicating how many of the 100 realizations are located at the same side of the original star. There should be also taken into account that the photometric error provided by the catalog is the error of the mean for those stars with more than one measurement, but is the error coming from the error propagation for the stars with a single measurement. So those errors will be analyzed independently (see Fig.8.5 and Fig.8.6 in Sect.8.1.3). Chapter 7

Testing distance derivation using Hipparcos data

In Sect.5 the different empirical calibrations available to compute physical parameters from Strömgren photometry have been studied. And in Sect.6.1, the atmospheric grids from the literature have been listed. In this section the capabilities of both methods (EC and MB) to derive stellar distances are analyzed using well studied Hipparcos stars having both, good parallaxes and Strömgren photometry. Since these Hipparcos stars are nearby stars, we will be checking the absolute magnitude calibrations, but not the derivation of the interstellar extinction. We will also check for systematic trends in distance and spectral types. The available classification methods will also be tested.

7.1 The Hipparcos sample

The working sample have 4765 OBA stars in all directions in the sky with Hipparcos parallaxes (ESA 1997) and Strömgren indexes (also with Hβ) from Hauck & Mermilliod (1998). The O and B stars have been obtained from the Torra et al. (2000) working sample (from the 6922 stars with astrometric data, only 2823 have all the photometric indexes and V magnitude available from Hauck & Mermilliod (1998)). For the A stars we use the sample from Asiain (1998) (where some restrictions have been applied for variable stars, stars in open clusters, etc). The final sample has 4765 OBA stars with both parallaxes and all photometric indexes. 164 of these stars have negative parallaxes and will be removed from the sample, leaving 4601. In Fig.7.1 we can see the distribution of parallaxes, distances, apparent V magnitudes and relative errors for those stars. The spectral type for those stars have been obtained from the Hipparcos Input Catalog (HIC hereafter) (mainly from Michigan spectral source, see Houk & Cowley (1975), Houk (1978), and Houk (1982)). This is a spectral method, so it could be more accurate than a photometric one. However, the limit between two regions is not well defined, e.g., the classification between a B9 and a A0 star is very difficult. In Table 7.1 we can see the number of stars available for each spectral type. Notice that the number of stars in region 3 is rather low.

91 92 CHAPTER 7. TESTING DISTANCE DERIVATION USING HIPPARCOS DATA

1400 800 1200 600 1000 800 400 # stars # stars 600 400 200 200 0 0 0246 81012 0 102030 V magnitude parallax (mas)

1400 800 1200 600 1000 800 400 # stars # stars 600 400 200 200 0 0 0 0.2 0.4 0.6 0.8 1 0 0.5 1 1.5 2 distance (kpc) relative error in parallax

Figure 7.1: HPC data distributions in V magnitude, distance, parallax and relative error in parallax.

Table 7.1: Number of Hipparcos stars in our sample from each photometric region. All O0-O9 B0-B9 A0-A3 A4-A9 4601 91 2568 1574 368

7.2 Classiﬁcation methods

We compare here the classification methods from Figueras et al. (1991) (FTJ91), Lindroos (1980) (LI80) and the new classification method (NC) (see Sect.5.1) with the spectral types provided by the HIC. In Tables 7.2, 7.3, 7.4, 7.5, and 7.6 we can see the comparison of the classification between the three methods and the HIC. In green we find the stars that are classified in the same region by the two methods. Stars in orange are due to missclassifications between consecutive regions, since limits between regions are very difficult to establish, e.g. difference between B9 and A0 star or between A3 and A4. On the other hand, stars in red show differences in the classification of more than one regions: these are usually stars located close to the gap and classified to early and late regions by different methods. Some important issues from Tables 7.2, 7.3, 7.4, 7.5, and 7.6 are:

• HIC only provide stars in the regions 0-3, since we selected only stars from O0 to A9. • FTJ91, LI80 and NC do not distinguish between O- and B-type stars, classifying all of them to region 1.

Table 7.2: Comparison between the classiﬁcations of HIC and FTJ91. HIC-FTJ91 1 2 3 4 5 0 115 0 0 1 0 1 2657 24 13 11 2 2 580 617 374 3 0 3 0 28 330 10 0 7.2. CLASSIFICATION METHODS 93

Table 7.3: Comparison between the classiﬁcations of HIC and LI80. HIC-LI80 1 2 3 4 5 0 108 7 1 0 0 1 2631 55 10 9 2 2 582 671 319 2 0 3 0 32 326 10 0

Table 7.4: Comparison between the classiﬁcations of HIC and NC. HIC-NC 1 2 3 4 5 0 108 0 0 1 7 1 2631 24 17 14 21 2 569 627 375 3 0 3 0 28 330 10 0

Table 7.5: Comparison between the classiﬁcations of FTJ91 and LI80. FTJ91-LI80 1 2 3 4 5 1 3319 33 0 0 0 2 1 668 0 0 0 3 1 61 655 0 0 4 0 3 0 22 0 5 0 0 0 0 2

Table 7.6: Comparison between the classiﬁcations of FTJ91 and NC. FTJ91-NC 1 2 3 4 5 1 3308 10 5 3 26 2 0 669 0 0 0 3 0 0 717 0 0 4 0 0 0 25 0 5 0 0 0 0 2 94 CHAPTER 7. TESTING DISTANCE DERIVATION USING HIPPARCOS DATA

• FTJ91 and LI80 results are very similar. However there are some discrepancies between both methods for some stars with low [c1] values, because LI80 classiﬁes them as region 2 and FTJ91 as region 3 (as we could see in Fig.5.2).

• Stars in region 2 according to HIC are the most difficult to classify. FTJ91 classify most of them to regions 1 or 3. From the 580 stars classified as region 2 by HIC and region 1 to FTJ91, 75% of them are A0 stars following HIC. On the other hand, almost 80% of the 374 stars classified as region 3 by FTJ91 are A2 or A3. Since the calibrations in these regions should be continuous this should not be a major issue.

• For MB methods we avoid the missmatch of classiﬁcation between regions 2 and others, since the method do not require previous classiﬁcation. We will only have the error between regions 1 and 3 (in the gap).

• As discussed in Sect.5.1 we will use the NC method. The region 1 stars missclassified as later group by this method are 1% while for FTJ91 are 0.5%. However we cannot check the missclassification in the opposite direction (later stars missclassified as region 1) because we do not have later stars in this sample.

The main conclusion is that it is very difficult to classify between regions, and we will be always missclassifying some stars at the edges between two regions. Missclassification between consecutive regions should not be very important since the calibrations should be continuous. These will be avoided by the MB method. The most important missclassification, present in both MB and EC methods will be between early and late regions.

7.3 Distance methods

We want to compare the photometric distances obtained using different methods with those provided by Hipparcos. But, since we want compare trigonometric and photometric distances, we should find the best way to do it. First, we have to take into account that we cannot directly compare distances since a symmetric error in trigonometric parallax is converted into a non-symmetric error in distances (see Luri & Arenou (1997)). In Fig. 7.2 we compare both distances (in this case for the CR78 photometric distance). As can be seen, there is a systematic trend in the sense that the photometric distances are smaller than HPC distances. This is well understood with the following argument: assuming, for simplicity, that the absolute error in Hipparcos parallax is constant and equal to Δπ= 0.001, one star at 200 pc (π=0.005) will have an asymmetric 1σ error in distance between [166, 250] pc. This asymmetry in the method explains how the observed Hipparcos distances -affected by errors- are larger than the photometric distances. The solution is then to compare directly the parallaxes, instead of the distances. As known, Hipparcos provided trigonometric parallaxes with their observed astrometric errors. Thus the error in the parallax (or the derived distance) do not depend on the parallax (or distance) itself. In contrast, when we work with photometric distances, the error in distance (or parallax) is depending of the distance (or parallax) itself. From Strömgren photometry we estimate a visual absolute magnitude with an error. This error then translate in a relative error in distance (or parallax). In Fig.7.3 we show an scheme of what we expect when comparing parallaxes:

• The absolute error in trigonometric parallax is constant. 7.3. DISTANCE METHODS 95

Figure 7.2: Diﬀerence in distance vs distance. In this case, as an example, comparison for region 1 stars, using Crawford method and Hipparcos distances.

• Since photometric distances (and parallaxes) have relative error, in absolute terms small distances have smaller errors that stars at larger distances.

• The resulting error of the diﬀerence (πpho − πhpc) will be the convolution of the two errors (see black curve in Fig.7.3).

• We have some stars with negative trigonometric parallaxes (less than 3% of the sample).

• Photometric parallaxes are always positive. Although statistically one should expect some negative values for small parallax due to the error, we force all the photometric parallaxes to be positive. This creates a forbidden region below the line of 45◦(see dashed line in Fig.7.3), because the differences (πpho − πhpc) will be always larger than -πhpc.Allthe stars that statistically could have fallen below that line, are forced to lay on πpho − πhpc=- πhpc. This creates a visual bias in the plots (see Fig.7.4-left). However, when we look for the median of this differences this trend will be avoided, since the median will only take into account the value of the central point, ignoring the values for the other stars. This effect would have been important if we had computed the average, so this is the reason (in addition of the rejection of the outliers) to use the median.

• It is better to plot the diﬀerences (πpho − πhpc) as a function of πhpc instead of πpho.The error in trigonometric parallax is constant along the horizontal axis, whereas the error in photometric parallax is not.

• To do the ﬁnal analysis we will avoid the stars with parallaxes smaller than πhpc <0”.003 (333pc). These more distant stars are fainter and will have larger errors in photometry. In addition they will be more aﬀected by interstellar extinction.

• In order to have a signiﬁcant number of stars in each region, we will use a diﬀerent limit for larger parallaxes. In region 1 we will avoid stars with πhpc >10 mas, in region 2 stars with πhpc >15 mas will be avoided, while the limit for region 3 will be πhpc =20 mas. 96 CHAPTER 7. TESTING DISTANCE DERIVATION USING HIPPARCOS DATA

Figure 7.3: Scheme of the expected distribution of πphot − πhpc.

• We will have other eﬀects that will modify the expected results, like errors in the photometry, large Hβ values due to emission line stars, ...

We can also study the differences in absolute magnitude MV , that is, try to minimize the differences in MV instead of parallax. This is equivalent to minimize the relative error in distance. And that implies that the further stars have less weight in final results. We can compute the MV from the photometry using the distance and the V magnitude like: MV = V − 5+5log(Dist) assuming null absorption (Hipparcos stars are very close), or using the excess provided by the method. We also expect that the distribution of excess E(b − y) should be close to zero, because of the assumed null absorption.

7.3.1 Empirical calibration methods (EC)

This methods require previous classification in regions. We need to compare the distances for each of the regions individually, since there are different empirical calibrations in each case. We have here two options, using the region as provided by HIC, or compute it from the FTJ91 method (that for Hipparcos stars is equivalent to LI80 and NC). We can also use for each region, only the stars that are classified in the same region by the two methods (in that case, we are avoiding all the stars at the edges between two regions). From now on we will compare the three options, that we will call:

• Classification from FTJ91 (F). It uses the Strömgren indexes for the classification. • Classification using HIC spectral type (H). • Only stars for which both classification match (HF). It is the safer classification, since we only take the star if it is classified in the proper region by both, the spectroscopic and photometric methods. The problem here is that we are removing all the stars at the edges between two regions, and we are removing the stars with some peculiar colors (or Teff ).

As we can see in Table 7.2, FTJ91 method classiﬁes more stars as region 1 (2657+580) than HIC (2657), so for that region, the HF method will be almost equivalent to H. On the other 7.3. DISTANCE METHODS 97

Figure 7.4: Difference in parallax vs Hipparcos parallax (left) and [c1] (right). From top to bottom, comparison of CR78, LI80 and BS84 with Hipparcos parallaxes. Region 1 stars selected by FTJ91. side, in region 2, we will find more stars following method H (580+617+374) than following F (617), so the intersection method HF will have equivalent results as the FTJ91 method. Finally, in region 3, F provides more stars (374+330) than H (330). Then, for each of the region we study each of the available methods. For region 1, we compare here the parallaxes obtained using Crawford (1978) (CR78), Craw- ford (1978) adding the Lindroos (1980) correction (LI80), and Balona & Shobbrook (1984) (BS84). Differences in parallax as a function of HPC parallax is in Fig.7.4. We plot the differences as a function of the Hipparcos parallaxes and also as a function of the [c1] index, that in this case is indicating Teff or spectral type. We see in that figure that results from CR78 and BS84 are very similar, and gives results pretty close to zero, although there is a clear trend in [c1]. For stars classified as region 2 (A0-A3), their distances can be computed following one of these methods: Claria Olmedo (1974) (CL74), Grosbol (1978) (GR78), Hilditch et al. (1983) (HI83), and Moon & Dworetsky (1985) (MO85). We show the comparison with Hipparcos distances in Fig.7.5 as function of Hipparcos parallaxes and also the index a =1.36 · (b − y)+0.36 · m1+ 0.18 · c1 − 0.2448 to check the color dependence because it is used to calibrate temperature in this region. We see in this case a trend in distance, but no trend in Teff . And for region 3 stars we can only compare with the method from Crawford (1979) (CR79), as can be seen in Fig.7.6, where we plot the differences in parallaxes as a function of the Hipparcos parallax and also the Hβ index, that traces effective temperature in this region. In Tables 7.8, 7.9 and 7.10 we can see, for the three regions, the median of the differences in parallax between the photometric and the Hipparcos values. We also subdivide each of the 98 CHAPTER 7. TESTING DISTANCE DERIVATION USING HIPPARCOS DATA

Figure 7.5: Diﬀerence in parallax vs Hipparcos parallax (left) and Hβ index (right). From top to bottom, comparison of CL74, GR78, HI83 and MO85 with Hipparcos parallaxes. Region 2 stars selected by HIC. 7.3. DISTANCE METHODS 99

Figure 7.6: Diﬀerence in parallax vs Hipparcos parallax (left) and Hβ (right). Region 3 stars selected by FTJ91.

Table 7.7: Number of stars used to compute the median for each of the groups and tests shown in Tables 7.8, 7.9 and 7.10 region 1 region 2 region 3 F H HF F H HF F H HF All 1674 1334 1302 All 512 1261 474 All 663 313 279 [c1] <0.2 107 102 100 a<0.05 179 568 169 2.85

regions in some sub-regions using the color index ([c1], a,andHβ) to check whether there is a trend in spectral type. The same tables show the diﬀerences in absolute magnitudes MV computed from Hipparcos data and through the photometric methods. Table 7.7 shows the number of stars available in each region and sub-region. We can see that in region 1 and 3 there are more stars in case of F selection than H and HF. In these cases, spectral types that have larger diﬀerences in the number of stars are the ones closer to region 2 (0.8< [c1] for region 1 and 2.85

Table 7.10: Median values of the diﬀerences in parallax and absolute magnitudes for all the region 3 stars with parallaxes between 3 and 20mas: πCR79 − πhpc MVCR79 − MVhpc F H HF F H HF All 0.56±0.12 0.60±0.17 0.62±0.18 0.11±0.03 0.11±0.04 0.11±0.04 2.85

In first approximation, we see in Fig.7.4-left the same features we detailed in Fig.7.3. For region 1 stars, we see in Table 7.8 a clear trend in effective temperature for all the methods. CR79 overestimates the distances for the hottest stars (B0-B4) and underestimates them for the latest group of B9 stars. One explanation could be the effect of the stellar rotation. As stated by Figueras & Blasi (1998), the rotational effects on the photometry can be important. They mentioned that rotation tends to decrease both, the effective temperature and the surface gravity. And that: ”photometric grids and other empirical calibrations (for instance, the unreddening procedures) are probably affected to some extent by all the rotating standard stars included in the samples”. We checked that there is no appreciable difference in the errors in parallax of the two samples of B0-B4 and B5-B9 stars, so that cannot be the reason either. They show almost equivalent distribution although the B4-B9 are a bit brighter (so slightly smaller error in the photometric parallax). CR78 and LI80 methods are pretty similar (in fact both methods only differ for some stars, those with 0.75

7.3.2 Comparing for diﬀerent atmospheric grids (MB method)

The model based method allows us to compute distances as we explained in Sect.6.1. In order to check those grids, we split sample in three photometric, following the photometric regions from FTJ91 (F), HIC (H) and both (HF), as we did for the empirical calibrations methods. But we must take into account that this method do not require this previous classiﬁcation, it has been done just to allow direct comparison with previous section. In Fig.7.7 we see the diﬀerences in parallaxes for the three regions, as a function of Hipparcos parallaxes and the index tracing Teff in each region (i.e. [c1],a,Hβ). Figure 7.8 shows the distribution of E(b − y)forthethree 102 CHAPTER 7. TESTING DISTANCE DERIVATION USING HIPPARCOS DATA

Table 7.11: Median values of the diﬀerence between parallaxes and absolute magnitudes for all the region 1 stars with parallaxes between 3 and 10”: πMB − πhpc MVMB − MVhpc F H HF F H HF All -0.41±0.06 -0.51±0.07 -0.51±0.07 -0.17±0.32 -0.22±0.42 -0.22±0.40 [c1] <0.2 -0.82±0.34 -0.97±0.34 -0.97±0.33 -0.14±3.71 -0.16±3.91 -0.21±3.79 0.2< [c1] <0.5 -0.42±0.11 -0.43±0.11 -0.21±3.79 -0.23±0.56 -0.23±0.56 -0.23±0.56 0.5< [c1] <0.8 -0.56±0.13 -0.56±0.13 -0.42±0.11 -0.27±0.49 -0.27±0.57 -0.27±0.51 0.8< [c1] -0.31±0.08 -0.39±0.11 -0.43±0.11 -0.13±0.19 -0.19±0.50 -0.19±0.38

Table 7.12: Median values of the diﬀerence between parallaxes and absolute magnitudes for all the region 2 stars with parallaxes between 3 and 15”: πMB − πhpc MVMB − MVhpc F H HF F H HF All 0.03±0.09 -0.28±0.07 0.03±0.09 -0.05±0.48 -0.10±0.50 -0.04±0.45 a<0.05 0.00±0.15 -0.16±0.08 0.00±0.16 -0.04±0.68 -0.07±0.22 -0.03±0.72 0.05

Table 7.13: Median values of the diﬀerence between parallaxes and absolute magnitudes for all the region 3 stars with parallaxes between 3 and 20: πMB − πhpc MVMB − MVhpc F H HF F H HF All -1.04±0.10 -1.33±0.16 -1.38±0.17 -0.39±0.03 -0.43±0.04 -0.45±0.04 2.85

Figure 7.7: Diﬀerences in parallax between MB method and Hipparcos vs Hipparcos parallaxes (left) and vs an index tracing Teff ([c1], a and Hβ). From top to bottom regions 1, 2 and 3 following the FTJ91 classiﬁcation.

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¤ ¤ ¤ ¤ ¤ ¤ ¤ E(b-y) E(b-y) E(b-y)

Figure 7.8: Distribution of excess E(b − y) for the MB method and for the three regions 1, 2 and 3 (from left to right). FTJ91 classiﬁcation. 104 CHAPTER 7. TESTING DISTANCE DERIVATION USING HIPPARCOS DATA

Table 7.14: Median values of the diﬀerence for all the region 3 stars with parallaxes between 3” and 20”. πMB − πHPC MVMB − MVHPC F H HF F H HF A -1.04±0.10 -1.33±0.16 -1.38±0.17 -0.39±0.03 -0.43±0.04 -0.45±0.04 B -0.17±0.11 -0.11±0.17 -0.11±0.18 -0.09±0.03 -0.08±0.04 -0.08±0.04 C 0.82±0.12 1.27±0.17 1.33±0.19 0.20±0.03 0.27±0.04 0.29±0.04 k=0.1 -0.07±0.11 0.01±0.17 0.02±0.18 -0.06±0.03 -0.03±0.04 -0.03±0.04 k=0.2 0.03±0.11 0.12±0.17 0.15±0.18 -0.03±0.03 0.00±0.04 0.01±0.04 k=0.3 0.12±0.11 0.27±0.17 0.33±0.18 0.00±0.03 0.04±0.04 0.05±0.04 k=0.4 0.26±0.11 0.43±0.17 0.48±0.18 0.05±0.03 0.07±0.04 0.09±0.04 k=0.5 0.39±0.11 0.55±0.17 0.63±0.18 0.08±0.03 0.12±0.04 0.12±0.04 k=0.6 0.49±0.11 0.74±0.17 0.79±0.18 0.12±0.03 0.16±0.04 0.17±0.04 k=0.7 0.58±0.11 0.87±0.17 0.93±0.18 0.15±0.03 0.19±0.04 0.20±0.04 k=0.8 0.67±0.11 1.01±0.17 1.09±0.18 0.18±0.03 0.22±0.04 0.23±0.04 k=0.9 0.74±0.11 1.15±0.17 1.19±0.19 0.19±0.03 0.24±0.04 0.27±0.04 the atmospheric grids used, that seems to be right for region 1 and 2, but shifted for colder stars. For this reason we repeat the checks using diﬀerent atmospheric grids, i.e. those from Smalley & Dworetsky (1995) and Smalley & Kupka (1997). These grids will only modify the results for stars with 5500

• A: Castelli & Kurucz (2006) (CK06)

• B: Smalley & Dworetsky (1995) (uvby) (SD95)+ CK06 (Hβ)

• C: Smalley & Dworetsky (1995) (uvby) (SD95) + Smalley & Kupka (1997) (Hβ) (SK97)

Since, as we will see, the best results are between options B and C, combination of both Hβ values is created like: Hβk = k · HβSD95 +(1− k) · HβCK06 (7.1) In Fig.7.9, Fig.7.10, Fig.7.11 and in Table 7.14 we see the results for all these grids. As we saw in previous sections, CK06 grids (option A) gives too low values (parallaxes are underestimated). On the other side, option C (SD95+ SK97) gives too large median values, and the best results are for option B (SD95+CK06). However, it seems that the best results should be between methods B and C, so this is why we check for the diﬀerent k coeﬃcients. Both, from Fig. 7.9 and Table 7.14, the best result seems to be between k=0.2. Also in Fig.7.11 we see that for this value the excess is well centered at zero. From now on we will use this value k=0.2 for the MB method computations. Table 7.15 shows the new median values 7.3. DISTANCE METHODS 105

Figure 7.9: Diﬀerence between photometric and Hipparcos parallaxes vs Hipparcos parallaxes. Orange line show the median values for 50 dots bins. Following FTJ91 classiﬁcation. 106 CHAPTER 7. TESTING DISTANCE DERIVATION USING HIPPARCOS DATA

Figure 7.10: Diﬀerence between photometric and Hipparcos absolute magnitudes vs Hβ values. Orange line show the median values for 50 dots bins. Following FTJ91 classiﬁcation. 7.3. DISTANCE METHODS 107

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Figure 7.11: Distribution in E(b − y) for all the grids. Following FTJ91 classiﬁcation. 108 CHAPTER 7. TESTING DISTANCE DERIVATION USING HIPPARCOS DATA

Table 7.15: Median values of the diﬀerence between parallaxes and absolute magnitudes for all the region 3 stars with parallaxes between 3 and 20”, using k =0.2 πMB − πhpc MVMB − MVhpc F H HF F H HF All 0.03±0.11 0.12±0.17 0.15±0.18 -0.03±0.03 0.00±0.04 0.01±0.04 2.85

7.4 Comparing model based and empirical calibration methods

In previous sections we compared the distances and absolute magnitudes that empirical calibrations and atmospheric model methods with those provided by the Hipparcos catalog, in order to choose the best options in each case. In this section the results from both methods are compared between them, using the stars in the Hipparcos working sample. For the empirical calibration method we will use the classiﬁcation method from Figueras et al. (1991), and then for each of the regions, Crawford (1978), Grosbol (1978), and Crawford (1979). On the other hand, for the atmospheric model method we will use the grids from Castelli & Kurucz (2006), plus the Smalley & Kupka (1997) for uvby and a combination of Castelli and Smalley & Dworetsky (1995) with k=0.2 (for 5500

Table 7.16: Median values of (b − y)andMV obtained from the two methods as a function of the HIC spectral type. N (b − y)0EC (b − y)0MB MVEC MVMB O5 9 -0.1292± 0.0009 -0.1267± 0.0081 -5.05±0.29 -3.82±0.42 O6 15 -0.1272± 0.0008 -0.1290± 0.0025 -5.11±0.26 -3.43±0.31 O7 18 -0.1277± 0.0006 -0.1264± 0.0031 -5.44±0.21 -3.41±0.28 O8 15 -0.1279± 0.0060 -0.1270± 0.0076 -6.11±0.56 -3.66±0.51 O9 49 -0.1255± 0.0006 -0.1216± 0.0026 -5.22±0.20 -3.40±0.24 B0 121 -0.1214± 0.0005 -0.1087± 0.0014 -5.34±0.12 -3.73±0.13 B1 184 -0.1172± 0.0007 -0.0997± 0.0012 -4.33±0.13 -3.43±0.14 B2 402 -0.0995± 0.0008 -0.0833± 0.0010 -2.84±0.11 -2.40±0.12 B3 256 -0.0824± 0.0015 -0.0692± 0.0016 -1.78±0.14 -1.53±0.14 B4 91 -0.0738± 0.0022 -0.0636± 0.0024 -1.34±0.25 -1.43±0.22 B5 266 -0.0684± 0.0010 -0.0580± 0.0010 -1.28±0.13 -1.40±0.13 B6 108 -0.0598± 0.0012 -0.0503± 0.0010 -0.82±0.16 -1.13±0.17 B7 135 -0.0523± 0.0014 -0.0469± 0.0015 -0.66±0.14 -1.05±0.14 B8 433 -0.0445± 0.0011 -0.0396± 0.0010 -0.37±0.08 -0.75±0.08 B9 609 -0.0341± 0.0013 -0.0260± 0.0014 0.56±0.06 -0.06±0.07 A0 684 -0.0147± 0.0017 -0.0080± 0.0017 1.06±0.03 0.57±0.05 A1 196 0.0018± 0.0029 0.0002± 0.0029 1.21±0.04 0.91±0.09 A2 419 0.0423± 0.0028 0.0595± 0.0030 1.24±0.05 1.06±0.07 A3 237 0.0700± 0.0037 0.0863± 0.0038 1.46±0.07 1.36±0.10 A4 58 0.0773± 0.0038 0.0957± 0.0038 1.17±0.12 1.00±0.22 A5 152 0.1110± 0.0040 0.1223± 0.0035 1.85±0.08 1.76±0.09 A6 13 0.1080± 0.0143 0.1191± 0.0117 1.85±0.38 1.72±0.80 A7 62 0.1215± 0.0055 0.1290± 0.0045 1.98±0.11 1.86±0.15 A8 38 0.1343± 0.0063 0.1400± 0.0052 1.96±0.17 1.86±0.23 A9 36 0.1690± 0.0078 0.1702± 0.0065 1.94±0.14 1.86±0.16 110 CHAPTER 7. TESTING DISTANCE DERIVATION USING HIPPARCOS DATA

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O5 O6 O7 O8 O9 B0 B1 B2 B3 B4 B5 B6 B7 B8 B9 A0 A1 A2 A3 A4 A5 A6 A7 A8 A9 SP

Figure 7.12: median values for the (b−y)0 and MV provided by the empirical calibration methods (red) and atmospheric models (blue) as a function of the HIC spectral type (from O5 to A9). Error bars show ﬁve times the error of the median.

Figure 7.13: Diﬀerences in (b − y)0 vs. the value obtained from the atmospheric models. Stars classiﬁed by FTJ91 method as region 1 in green, in region 2 in blue and in region 3 in red. 7.5. CONCLUSIONS 111

Figure 7.14: Diﬀerences between MB and HPC distances vs HPC distances. Red lines show the moving median.

Figure 7.13 shows the differences in intrinsic color for both methods. Some of the stars classified as region 3 by FTJ91, have colors according to region 2 stars as computed by MB (the group of red stars in the top of the plot). Considering the HIC spectral type for these stars, they are (more than 90% of them) in the range A0-A3, so it seems that MB methods are classifying them better than the FTJ91 method. There are no stars missclassified between regions 1 and 3 (in the gap). From Fig.7.14 we see that there is a small trend between EC and MB distances. As we can see in Tables 7.8, 7.9 and 7.10, the differences in parallax between EC and Hipparcos were positive for the methods we are using. That leads to a small overestimation of the EC parallaxes, i.e., an underestimation of the distances, that matches with the results in Fig.7.14: MB distances are larger than EC distances.

7.5 Conclusions

The parallaxes and absolute magnitudes obtained from the Hipparcos catalog have been used to test the EC methods available and chose, for each region, those that provide better results. They also have been used in order to improve the MB method choosing the grids that fit better with the Hipparcos data. Table 7.17 shows the main results of the comparisons, with the obtained shifts and trends. The EC methods that have been chosen for each region, and that will be used from now on will be CR78 for region 1, GR78 for region 2 and CR79 for region 3. We see in general a bias in the EC methods providing parallaxes larger than those from Hipparcos (smaller distances). This mean shift can be different if we choose a different set of stars, since an important trend in Teff is present.

The results obtained for the MB method are better because there is no trend in Teff and the shifts are similar or even smaller. In addition, by using this method we avoid the problems we can have with the classifications, with no discontinuities between the different regions. One issue present in both EC and MB methods that can lead to important discrepancies is the stars in the gap, i.e., stars between regions 1 and 3, with [m1] ∼0.15-0.20. Small shift or error in the photometry of these stars may lead to missclassifications, and so, to large errors in the distance, because it will be treated as a hot (B-type) or cold (A-F-type) star. 112 CHAPTER 7. TESTING DISTANCE DERIVATION USING HIPPARCOS DATA

Table 7.17: Mean results of the comparison between HPC data and photometric model physical parameters. EC method MB method region 1 CR78: Δπ ∼ 0.4mas. ΔMV ∼ 0.15. Trend in Teff . No trend in Teff LI80: Δπ ∼ 0.6mas. ΔMV ∼ 0.20. Trend in Teff . Δπ ∼-0.4mas BS84: Δπ ∼ 0.2mas. ΔMV ∼ 0.06. Trend in Teff . ΔMV ∼ -0.2 region 2 CL74: Δπ ∼ 0.45/-0.15mas. ΔMV ∼ 0.1/-0.05. Trend in π. No trend in Teff GR78: Δπ ∼ 0.45/-0.15mas. ΔMV ∼ 0.15/-0.05. Trend in π. Δπ ∼0./-0.2mas HI83: Δπ ∼ 0.5/-0.1mas. ΔMV ∼ 0.15/-0.05. Trend in π. ΔMV ∼0./-0.1 MO85: Δπ ∼ 0.55/-0.05mas. ΔMV ∼ 0.17/-0.03. Trend in π. region 3 CR79: Δπ ∼ 0.6. ΔMV ∼ 0.11. Trend in Teff . Using k=0.2 Δπ ∼0.1 ΔMV ∼0.01

Another bias that can be present in the MB method is for the stars in region 2, close to the turning point of the grids. In that position, small errors in the photometry moving the stars downwards in the [c1] − [m1] diagram will lead to a classiﬁcation of the star at the left or right side of the peak, and so decreasing the number of stars that are matched with the peak of the grid. A diﬀerent problem present in the methods that involve grids, (for the MB model, but also some EC methods that are interpolating in tables) are those points that fall outside the grid. They are shifted to the edges of the grid leading to overdensities in some regions that are not real. Chapter 8

Application to our catalog

The methods described in chapters 5, 6 and 7 are applied here in order to characterize the stars in our photometric survey. The distribution of the physical parameters for the stars in our sample that have all the six photometric indexes available are presented here. A detailed statistical analysis of the errors in the derivation of these physical parameters is also included. In addition, we also compare the results obtained using both, EC (see Sect.5) and MB (see Sect.6) methods. The methods are only checked for stars until A9 (photometric regions 1, 2 and 3), so stars hotter than Teff ∼7000K. From now on, when discussing the results of the MB method we will only take into account these 13337 stars, that are 37% of the total sample. We leave for future studies the derivation of physical parameters of cold stars. For our study of the anticenter we only need stars until A3 (that have Teff ∼8500K), so in principle we do not need to extent the classiﬁcation beyond Teff ∼7000K. On the other hand, when discussing the results of the EC model we will only consider the stars classiﬁed as region 1, 2 and 3 by FTJ91 method, for the same reasons discussed for MB method. This group of stars are a 33% of the sample.

8.1 MB method

8.1.1 Probability

As we discussed in Sect.6.6.3 the 3D fitting with the atmospheric grid is developed through a P probability parameter. Maximizing this parameter for all the points of the grid we obtain the best point for the fitting. In Fig.8.1 we see the maximum probability distribution (Pmax)for all the stars (Pmax=0.32 means that the maximum probable point of the grid is at 1Dse of the star). We are using all the stars with Teff >7000K. As we can see there are several stars with Pmax very close to zero. That means that the grid and the star are too distant, and we cannot match that star with any of the points of the grid, due probably to the fact that the errors in photometry are underestimated. The relation between the distance grid-star (Dgs)andthe photometric error of the star in that direction (Dse) is directly related with the probability, as we −7 can see in Fig.8.2. Stars with Pmax < 5.7·10 have the most probable point of the grid located further than 5Dse. There are 0.01% of the stars like that, which we can consider as wrong assignations. This very low probability can be due to two different causes. Either the errors are underestimated (low Dse), or they can be outliers, peculiar stars that have photometric indexes

113 114 CHAPTER 8. APPLICATION TO OUR CATALOG

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¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ P logP

Figure 8.1: Histogram of the probability parameter. Right plot column shows the log P in order to check the bins close to zero.

Figure 8.2: Dse vs. Dsg. Pmax parameter is color-plotted.

that lay too far from the grid (large Dgs) (like binaries, variable stars, etc.). Through these three parameters Pmax, Dse and Dgs we can check whether the star is correctly assigned.

−7 • Pmax > 5.7 · 10 : good assignation.

−7 • Pmax < 5.7 · 10 : wrong assignation due to:

-lowDse and large Dgs: possible outlier.

- large Dse and low Dgs: error underestimated.

Stars located in the gap between early and late type regions will have a similar probability to belong to either side. We always assume as valid the point of the grid with maximum probability, but in this cases it is worth to keep also the maximum probability this star would have if it was (B) assigned at the other side of the gap. We call this second probability index Pmax.Iftherelation (B) Pmax/Pmax is close to 1, we cannot be sure which is the correct assignation. 8.1. MB METHOD 115

4000 4000 3500 3500 3000 3000 2500 2500 2000 2000 1500 1500 1000 1000 500 500 0 0 3.8 3.9 4.0 4.1 4.2 4.3 4.4 4.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 log(Teff) logg

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Figure 8.3: Distribution of physical parameters for the 13337 stars in our catalog with all the photometric indexes available and Teff >7000K computed using the MB method.

8.1.2 Physical parameters

Figure 8.3 shows the distribution of diﬀerent physical parameters of our catalog stars with Teff >7000K.Inthelog(Teff ) histogram there is a decrease that correspond to the cut in Teff . Most of the stars have gravities in the range log g=4-5, i.e. main sequence stars. There are few stars with very low gravities i.e. giants and supergiants. Some of them are coming from stars that are far of the grid and that are assigned to the edges of the grid, so they could also be wrong assignations or outliers. There are ∼57% of the stars which have zero age, so can be located in the ZAMS. Only those stars with age diﬀerent to zero are plotted in the age histogram. Due to the cut in Teff set, there is also a cut in absolute magnitude MV around 3.5, corresponding to a ∼F3 type star. 116 CHAPTER 8. APPLICATION TO OUR CATALOG

100

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Figure 8.4: Nside in a [c1] − [m1]plot.

8.1.3 Errors

As explained in Sect.6.7 the errors for all the physical parameters are computed using Montecarlo simulations. There were generated 100 simulated realizations for each star using the original errors in the V ,(b − y), m1, c1,andHβ photometric indexes. The errors are computed like the dispersion obtained for the output parameters from all the simulated realisations. However the stars located close to the gap can have some of the realizations at the other side of the gap, so with very diﬀerent temperatures and physical parameters. Since that would increase substantially the error in all the physical parameters, only the stars located at the same side of the gap of the original star (measure without adding any random error) are used for the error computation. That is, if both, the original star and the current i realization have [c1] >0.85 the current realization is considered for the error. This limit as 0.85 has been set empirically taking into account the turning point of the grid sequence. If one of them or both have [c1] <0.85, then we will consider it for the error computation only if both have Teff either larger or smaller than 10000K. The number of realizations (from the 100 set) used for this error computation is called Nside and will give us a measure of how probable is that the star belongs to that side of the gap. That factor will depend on the location of the star in the [c1] − [m1] − Hβ space and also on the photometric errors. We can see in Fig.8.4 the distribution of the parameter Nside in an [c1] − [m1] diagram. On the other hand we also computed the maximum probability for a star to belong at both (B) sides of the gap, that is Pmax is the absolute maximum probability, and Pmax is the maximum probability at the other side of the gap (i.e., if Pmax is for a point with Teff <10000K,then (B) Pmax will be for a point with Teff >10000K and viceversa). That second probability will not have much sense for stars very close to Teff =10000K, or really far from the gap. But it will be (B) important for stars with the two probabilities being very similar, so a star with Pmax/Pmax ∼1 will be a star that can be placed in both sides with similar probabilities, and so will have a Nside value close to 50%. 8.2. EC METHOD 117

We have to take into account that the error provided in the catalog for the photometric indexes is the error of the mean for the stars with more than one measurement but it is the dispersion from the error propagation in case of a single measurement stars. We split the sample in two diﬀerent sets, on one hand the stars with a single measurement (32%), and the stars with more than one measurement (68%). We plot the errors in both cases in Fig.8.5-8.6. In general we see that the errors for the stars with a single measurement are larger. This can be due to the photometric errors of the mean for the stars with only one measure can be slightly underestimated. In addition, stars with one measurement tend to be fainter, since for these stars some measurements may be missed. Almost all the stars have relative error in Teff smaller than 10%, and the error in log g smaller than 0.5dex. Errors in absolute magnitudes are slightly larger, reaching up to 0.5mag for few stars, and errors in AV can reach 0.1-0.2. Finally the relative error in distance seems to be smaller than 10-20% for stars with more than one measure and can reach up to 30-40% for stars with a single measurement.

8.2 EC method

8.2.1 Physical parameters

The EC method classiﬁed the stars in diﬀerent regions (we used the NC method for that purpose, see Sect.5.1). And then the physical parameters were computed only for stars with photometric types until A9 (i.e. photometric regions 1, 2 and 3). In Fig.8.7 we can see the physical parameter distribution for all these stars.

The MV distributions are not exactly as expected, since they have mean absolute magnitudes fainter for each of the regions. For early-type stars we would expect absolute magnitudes up to MV ∼0, but we get MV up to 2 for some stars. Something similar happens with region 2 and 3, for which the expected range of absolute magnitudes are 0-1.5 and 1.5-3, respectively.

8.2.2 Errors

The errors are again computed through 100 random realizations and through gaussian errors in the V,(b − y),m1,c1 and Hβ photometric indexes. Since the stars are first classified in the photometric regions, we need to compute how many random realizations are located in the same region than the original star: Nreg. See the distribution for this parameter in Fig.8.8. We will only use the realizations located in the same regions than the original star for error computation. In addition, and since there are five different possibilities, we computed for each star how many of the 100 random realizations fall in each of the regions, through the values Nreg1, Nreg2, Nreg3, Nreg4,andNreg5. We see the results plotted in Fig.8.9. We do not plot the Nreg5 since it is only important for stars with Teff colder than 7000K. In Fig.8.10 we can see the distribution of errors for different physical parameters in two cases, stars with one and more than one measurement. In general, we see that the obtained errors are larger than the ones obtained by the MB method (see Fig.8.6). 118 CHAPTER 8. APPLICATION TO OUR CATALOG

Figure 8.5: Distribution of errors. Black lines show the moving median for each plot. From to to bottom relative error in Teff ,logg, MV , AV and relative error in distance. Left: Disper- sions for stars with only one measurement. Right: dispersions of the stars with two or more measurements. 8.2. EC METHOD 119

2500 500 2000 400 1500 300 N N 200 1000

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0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.1 0.2 0.3 0.4 0.5 © © dist/dist dist/dist

Figure 8.6: Distribution of errors. From to to bottom relative error in Teff ,logg, MV , AV and relative error in distance. Left: Histograms for stars with only one measurement. Right: Histogram of the stars with two or more measurements. 120 CHAPTER 8. APPLICATION TO OUR CATALOG

All 0-B9 A0-A3 A4-A9 1600 2500 3000 1200 1400 2500 2000 1200 1000

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0 0 0 0 0 1 2 3 4 5 6 0 1 2 3 4 5 6 0 1 2 3 4 5 6 0 1 2 3 4 5 6 AV (mag) AV (mag) AV (mag) AV (mag)

Figure 8.7: Distribution of physical parameters for all the stars in our catalog with all the photometric indexes available. In red, histogram for all the stars in the range B0-A9, and in other colors, individual regions computed by NC method. Parameters computed using the EC method.

Figure 8.8: Nreg parameter in a [c1] − [m1]plot. 8.2. EC METHOD 121

Figure 8.9: Nreg1,Nreg2, Nreg3 and Nreg4 parameters in [c1] − [m1]plots. 122 CHAPTER 8. APPLICATION TO OUR CATALOG

700 2000 600 500 1500 400

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N N 1000 300 200 500 100 0 0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 0.0 0.2 0.4 0.6 0.8 1.0

/distance /distance

dist dist

Figure 8.10: Errors distribution in MV , AV and distance computed by EC for stars with a single measure (left) and more than one measure (right). 8.3. COMPARISON BETWEEN EC AND MB METHODS 123

Figure 8.11: Diﬀerence in (b − y)0 between the two methods (EC minus MB) vs MB color. Photometric region according to NC is color-plotted.

8.3 Comparison between EC and MB methods

The catalog in the anticenter is used here to compare the physical parameters obtained using the two methods, MB and EC. Fig.8.11 shows the differences in intrinsic color (b − y)0 between the two methods. Photometric region according to NC is color-plotted. As we can see, most of the stars lay around zero, with a group of stars that have differences in (b − y)0 clearly larger. The red stars above the main trend are classified as region 3 by NC, but have (b − y)0MB < 0, so matching with region 1 stars. That is, the two methods are classifying them at the two sides of the gap, one to region 1 and the other to region 3. They are ∼8% of the stars. On the other hand, there are some blue stars at the bottom part of the diagram classified as region 2 by NC, but located at the right part of the gap (region 3) following the MB method. They are less than ∼0.5% of the stars. These stars are located in the gap between regions 1 and 3, and classified differently by the two methods. Have these stars larger photometric errors than the other stars? We did not notice a decrease of the fraction of missclassified of stars by reducing the photometric error, nor selecting only the stars with larger number of observations. However we detected that the missclassified stars have a mean magnitude slightly fainter than the good ones (see Fig.8.12). There is no proper way to know, for these stars, which is the good classification. The only way is to keep track of both solutions, and at the end select the most probable one, and also study the possible errors. From now on we will not use these inconsistent stars when comparing the physical parameters because it is pretty clearly that they will be very different in Figs. 8.13, 8.14, 8.15 . Fig.8.13 shows the differences in distance between the two methods, that can reach 20%. The EC method gives clearly smaller distances than the MB method. These deviations were already observed in Chapter 7 using Hipparcos data. There, the differences were from the computation of MV since they were nearby stars and the absorption was negligible. In this case, since the stars are much further, the differences in absorption also play an important role. Figs. 8.14 and 8.15 show the differences in AV and MV respectively, presenting a bias in 124 CHAPTER 8. APPLICATION TO OUR CATALOG

0.40

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0.25

0.20

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0.10

0.05

0.00 10 11 12 13 14 15 16 17 18 V magnitude

Figure 8.12: Normalized histogram of the V magnitudes. In green, the stars classified in the same region by both methods. In red, stars classified at the different side of the gap by NC and MB methods.

the correct direction, that is, AVEC >AVMB and MVEC >MVMB, both leading to an increase of the differences in distance. However, the differences in absorption are smaller than ∼0.05 magnitudes, while the differences in absolute magnitude reach values close to 0.5 magnitude. So the differences in distances are mainly due to the different calibrations for MV . 8.3. COMPARISON BETWEEN EC AND MB METHODS 125

Figure 8.13: Diﬀerence in distance between the two methods (EC minus MB) vs MB distance. From top to bottom, all the stars with EC distance available, stars classiﬁed by NC as region 1, region 2 and region 3. 126 CHAPTER 8. APPLICATION TO OUR CATALOG

Figure 8.14: Diﬀerence in absorption computed by the two methods (EC minus MB) vs MB distance. From top to bottom, all the stars with EC distance available, stars classiﬁed by NC as region 1, region 2 and region 3. 8.3. COMPARISON BETWEEN EC AND MB METHODS 127

Figure 8.15: Diﬀerence in absolute magnitude computed by the two methods (EC minus MB) vs MB distance. From top to bottom, all the stars with EC distance available, stars classiﬁed by NC as region 1, region 2 and region 3. 128 CHAPTER 8. APPLICATION TO OUR CATALOG

Figure 8.16: Left: RA-DEC plot. In green stars with IPHAS data available. Right: Hα vs. Hβ. In red, stars classiﬁed as emission line. Green line shows the limit established.

8.4 IPHAS

Only half of our survey area is covered by the IPHAS initial data release (IDR) (Gonz´alez- Solares et al. 2008). Up to 19490 of the 35974 stars in our survey with full photometry have IPHAS data (see Fig.8.16-left). These data allows us to detect emission line stars through the (r − Hα) index (see in Fig.8.16-right). We consider that a star is emission line when (r − Hα) > −0.614Hβ +2.164. We include a ﬂag EMLS in the catalog being 0 when the star is not an emission line star, 1 when it is, and 2 if we do not have IPHAS information for this star. Around 5% of the stars with IPHAS data turn out to be emission line. As explained in Sale et al. (2010), the distance and extinction for early-A stars (A0-A5) can be estimated using the IPHAS color-color plot: (r-i) vs. (r-Hα). The steps proposed by the authors we have followed to compute the IPHAS distance and AV for our stars are:

1. The main sequence in the (r-i) vs. (r-Hα) has a minimum in A0, and the interstellar absorption only moves the sequence up and right (see Fig.6 from Sale et al. (2010)). So the line that contains the A0 stars is ﬁtted to:

(r − Hα)=−0.009 + 0.330(r − i) − 0.0455(r − i)2 (8.1)

The stars contained between this line and the same line shifted by Δ(r − Ha)=0.03 are assumed to be early-A stars. 2. Assuming an intrinsic color for those stars of (r − i)=0.06 we can compute the interstellar absorption as Ar =4.13 · E(r − i).

3. Adopting Mr=1.5 the distances are computed like: − − D =10(r Mr+5 Ar)/5 (8.2)

Fig. 8.17 shows the selection of the early A-type stars from our catalog using IPHAS data, as well as their visual absorption computed as AV =4.01 · E(r − i). We also present the 8.5. 2MASS 129

Figure 8.17: Top-left: selection of the early-A stars of our sample through the (r − Hα)vs.(r − i) IPHAS plot. The two black curves show the main sequences for E(B-V)=0 and E(B-V)=1 (data obtained from Drew et al. (2005)). Red lines show the A0 sequence and the limit for early-A type stars selection (A0 sequence plus a vertical shift of 0.03 mag). Top-right: right ascension vs. declination (in degrees) distribution of the stars in our sample having visual absorption from IPHAS. Bottom-left: differences between MB and IPHAS distances as a function of MB distance. Bottom-right: difference between MB and IPHAS visual absorption AV . comparison between distance and absorption obtained through IPHAS with that obtained using the MB method. There is a clear bias between both methods that can reach differences up to 30% in distance.

As can be seen in Fig.8.17-bottom-right, a clear trend is observed when plotting (AV,IPHAS − AV,MB) against distance in the sense AV,IPHAS

8.5 2MASS

Almost all the stars in the anticenter survey have 2MASS counterpart (35730 of the 35974). The J, K,andK photometry allows us to work with red magnitudes, that are less affected by extinction. We can see in Fig.8.18 the differences in astrometry are much smaller than 0.5. 2MASS indexes are also affected by extinction, so they are not useful to distinguish between 130 CHAPTER 8. APPLICATION TO OUR CATALOG

Figure 8.18: Diﬀerences in α cos δ and δ between our catalog and 2MASS.

diﬀerent regions or diﬀerent type stars. However, once we have the AV absorption obtained from both, the MB and EC methods, we can obtain the absorption in the 2MASS infrared indexes using the transformations described in Rieke & Lebofsky (1985):

AJ =0.282AV (8.3)

AH =0.175AV

AK =0.112AV

With that we can compute the extinction corrected indexes (J − H)0,MB,(J − K)0,MB,(J − H)0,EC and (J −K)0,EC corresponding to each of the methods. And we compare these obtained values with the expected main sequence colors obtained for the Johnson values (Bessell et al. 1998). We are assuming here that the 2MASS and Johnson colors are equivalent. For stars not in the main sequence, the photometry can vary up to ∼0.05 mag for hot stars. In Fig.8.19-top we can see the distributions in the (J −H)0,MB vs. (b−y)0,MB and (J −K)0,MB vs. (b−y)0,MB for our stars and the expected main sequence. In these planes, we can compute the minimum distance between the location of the un-reddened star and the expected main sequence:

2 2 DJK,MB,min = ((b − y)0,MB − (b − y)MS) +((J − K)0,MB − (J − K)MS) (8.4)

2 2 DJH,MB,min = ((b − y)0,MB − (b − y)MS) +((J − H)0,MB − (J − H)MS)

2 2 DJK,EC,min = ((b − y)0,EC − (b − y)MS) +((J − K)0,EC − (J − K)MS)

2 2 DJH,EC,min = ((b − y)0,EC − (b − y)MS) +((J − H)0,EC − (J − H)MS)

A very large value for these indexes is indicating that the Str¨omgren photometry is not coherent with the 2MASS photometry. As explained before, for the MB method, we also computed the physical parameters considering that the star should be located at the other side of the gap (case B, see Sect.6.6.3). Using this absorption AV,B we can compute the unreddened color indexes, for case B: (J − H)0,B and 8.5. 2MASS 131

(J − K)0,B. And we can also compute the distance to the main sequence, in this case:

2 2 DJK,B,min = ((b − y)0,B − (b − y)MS) +((J − K)0,B − (J − K)MS) (8.5)

2 2 DJH,B,min = ((b − y)0,B − (b − y)MS) +((J − H)0,B − (J − H)MS)

Then, in order to check which of the two sets of unreddened indexes (i.e., the assigned by MB or the case B ones) ﬁt better with the expected main sequence, we compare the two computed distances through the ﬂags:

FlagJK = DJK,B,min − DJK,MB,min (8.6)

FlagJH = DJH,B,min − DJH,MB,min

We expect that the original MB parameters will be better than the case B ones, i.e. DJK,MB,min < DJK,B,min and DJH,MB,min

Figure 8.19: Top-left: (J −K)0 vs. (b−y)0. Black line is the expected main sequence. Top-right: (J − H)0 vs. (b − y)0. Bottom-left: FlagJK vs. FlagJH. In red, stars with FlagJK + FlagJH < −0.1. In green, stars with FlagJK + FlagJH < −0.2. Bottom-right: [m1] − [c1]plotthatshow the location of the green and red stars. Part IV

THE PERSEUS SPIRAL ARM

133

Chapter 9

Stellar content in the anticenter

9.1 The catalog of young stars

In previous chapters we have built a photometric catalog in the anticenter direction of 35974 stars with full photometric indexes and physical parameters. In order to use these data for the detection of the Perseus arm we create different working samples by giving different priority both to the quality of the data and to their completeness. Since we have followed two different approaches to compute physical parameters (see Chapters 5 and 6), the conditions to clean the samples will be different for each of them. We use also external data (IPHAS and 2MASS) to define the best accurate working sample. The full scheme is presented in Fig.9.1.

Rejection of emission line stars using IPHAS

As mentioned in Sect.8.4, around half of our stars have IPHAS data. We have used this information and the criteria described in Sect.8.4 to remove emission line stars. 1073 stars have been eliminated, with 34901 still in the sample. Note that not all the emission line stars are detected here, because the IPHAS information is missing for around half of the sample.

Hot stars selection

For the study of the Perseus arm, we need stars bright enough to reach completeness at large distances, so cold stars have to be rejected from the sample. As discussed in Chapter 6 the MB method has been fully tested and implemented only for stars with Teff >7000K. This has been the condition imposed for the ﬁrst selection of the hot population. For the EC method, we only considered physical parameters for stars from regions 1, 2 and 3, i.e. until A9 spectral type. The two samples created from these selections are:

• MB-S1: 12957 stars with Teff >7000K (MB method). • EC-S1: 11524 stars from regions until A9 (EC method).

There are 11187 stars in common between MB-S1 and EC-S1. 14% of the stars in MB-S1 are not in EC-S1; these are stars classiﬁed at later regions (4-5) in the EC method, but located at the early region (B-type stars) by MB. They are stars in the gap at the [c1] − [m1]plot,soas

135 136 CHAPTER 9. STELLAR CONTENT IN THE ANTICENTER

Figure 9.1: Scheme showing the procedure for the generation of the working samples. From top to bottom, the number of stars in the samples decrease while the quality of the individual physical parameters increases. Left side shows the samples according to MB method, and right side shows for EC. 9.1. THE CATALOG OF YOUNG STARS 137 discussed in Sect.5.1 the two methods classify them in very diﬀerent regions.As will be seen, we will be able to re-classify some of these stars by using the 2MASS data (see below). In addition, 337 stars are in EC-S1 but not in MB-S1. Looking at their position in the [c1] − [m1]plot,most of them look like late stars.

Rejection of outliers

Only 53 stars have Pmax < 5Dse (see Sect.8.1.1). These are outliers, with very low probability Pmax parameter, so they are very diﬃcult to assign to a any point of the grid by the MB method. They can be both, stars very far from the grid (large Dsg) or closer to the grid but with very small errors (low Dse). 12904 stars remain in the MB sample.

Monte Carlo assignment criteria

In order to remove the stars with doubtful classification, we use the parameters Nside and Nreg. They are defined as the number of times, for the 100 Monte Carlo random realizations for the error computation (see Sect.5.4 and 6.7), they fall in the most probable side of the [c1] − [m1] diagram (for MB) and in a given photometric region according to NC (for EC) respectively. We use a limit of Nside >70 for the MB method, so the stars with smaller values are assumed to have doubtful classification and are rejected. For the EC method, we only want to avoid the differences between regions 1-3, 1-4, etc., so no between consecutive regions, so we use the following conditions:

• For region 1 stars: Nreg1 > 70 or Nreg1 + Nreg2 >90.

• For region 2 stars: Nreg2 > 70 or Nreg1 + Nreg2 + Nreg3 >90.

• For region 3 stars: Nreg3 > 70 or Nreg2 + Nreg3 + Nreg4 >90. There are 2365 stars rejected in the MB method and 1585 in the EC case. Note that this criteria is very restrictive removing ∼18% and ∼14% of the MB and EC sample respectively.

2MASS data

As discussed in Sect.8.5, almost all our stars have 2MASS data. The indexes used here to clean the sample were defined using a color-color diagram combining 2MASS and uvbyHβ photometry (see Sect.8.5). For the MB method we compute the FlagJK and FlagJH indexes, to look for the most probable classification according to the 2MASS data. As stated, a very negative values of these indexes, indicate that the ”non-assigned” classification is better. We have decided to reject the stars with FlagJK + FlagJH < −0.1 (574 stars). In addition we have used distance between the location of the star and the expected location in a theoretical main sequence as an additional selection criteria. When the distance is very large, the coherence between 2MASS and the Strömgren photometry is low. Since the limit is highly dependent on the magnitude, a magnitude dependent function is used, setting the 2 2 − · 2 2 limits to: DJK,MB,min + DJH,MB,min < 0.16 + 0.22 V and DJK,EC,min + DJH,EC,min < −0.16 + 0.22 · V , for MB and EC, respectively. 184 and 317 stars are rejected due to these limits for MB and EC respectively. As can be seen in Fig.9.1, the remaining samples are named MB-S2 (with 9781 stars) and EC-S2 (with 9622 stars). 138 CHAPTER 9. STELLAR CONTENT IN THE ANTICENTER

Table 9.1: Number of stars for the samples deﬁned in Fig.9.1, and also for the inner and outer sky areas. MB-S1 EC-S1 MB-S2 EC-S2 CS inner 7763 6756 6061 5943 4998 outer 5194 4768 3720 3679 3103 all 12957 11524 9781 9622 8101

Clean sample

Up to now, the MB and EC samples have been cleaned using different criteria. we have created an even more cleaned sample by crossmatching the two samples MB-S2 and EC-S2. There are 8328 stars in common. | − MB − − CR| We have also rejected the stars for which: (b y)0 (b y)0 > 0.1, because this could indicate a different classification between the two methods. These are mainly stars classified in region 2 and 3 by different methods (see Fig.8.11 in Sect.8.3). The final clean sample (CS from now on) has 8101 stars. For each of the five samples described here, we can split them between the inner (i.e. deeper) sky area and outer (i.e. shallower) area (see Sect.4.4.4). In Table 9.1 we can see the number of stars in each of these sub-samples.

9.2 Limits on apparent magnitude

For each of the five samples described in Sect.9.1 (see Fig.9.1), we need to evaluate the apparent visual limiting magnitudes up to which they are complete both in the faint and in the bright end. We split the samples between the inner (and deeper) area, and the outer (and brighter) sky area, according to the observational strategy defined in Sect.4.1 (see Table 9.1). We can see the visual magnitude distribution for the inner and outer areas of the MB-S1 sample in Fig.9.2. The faint visual limiting magnitude is computed as the mean of the magnitudes at the peak star counts in a magnitude histogram and its two adjacent bins, before and after the peak, weighted by the number of stars in each bin. As explained in Sect.4.4.4, we estimated that the limiting V magnitude computed with this simple algorithm provides the 90% completeness limit. The resulting values are in Table 9.2. The different samples have a limiting magnitude V ∼16.7 for the inner area and V ∼15.7 for the outer area, except for the most clean sample, for which V ∼16.3 and V ∼15.3 respectively. As we discussed in Sect.4.4.2, the brightest stars in the sample can suffer from saturation. We have fixed the magnitude where some stars start to have saturation problems around Vsat =11- 11.5, where several stars will be lost due this effect. In order to check for the absolute completeness in V magnitude in terms of star counts of our working samples, we compare with the deeper sample we have, that is the full catalog with V magnitudes (95255 stars, see Table 4.4). We analyze separately the inner and outer sky areas. We plot in Fig.9.3 the ratio as a function of V magnitude between the two histograms, the most complete one and the S1 samples.Then in Fig.9.4 we see the ratios of the other samples with the S1 samples, i.e., S2/S1 and CS/S1. The ratio should be more or less constant for bright stars, and it starts decreasing when the sample is not complete. We are assuming here that the two 9.3. LOOKING FOR A POPULATION COMPLETE UP TO 3 KPC 139

200

150 2 o

100 # stars/

0 10 11 12 13 14 15 16 17 18 19 V magnitude

Figure 9.2: V magnitude distribution for MB-S1 sample, inner (blue) and outer (green) sky areas in stars per square degree. populations are similar, and so they have the same star density as a function of the distance. As we can see in the figure, the ratio for bright magnitudes is not so flat as we could expect, probably due to the fact that the different cuts and selections of stars are not completely uniform in apparent magnitude. But there is a clear change of slope at a given magnitude that matches approximately the Vlim fixed through the previous method (mean of the peak bins). The ratio given in the y axis of Fig.9.3 is the factor of stars that have been lost when selecting the stars with all the filters available, and other cleaning criteria described in the previous section. In Fig.9.4 we see the ratios of the other samples with the S1 samples, i.e., S2/S1 and CS/S1, so the ratio of stars lost when cleaning the samples.

9.3 Looking for a population complete up to 3 kpc

For the samples deﬁned in Sect. 9.1 we need to extract the subsamples surely complete up to 3 kpc (since the maximum distance expected for the position of the spiral arm is around 2.5- 3 kpc). These subsamples will be created imposing a limit of the intrinsic brightness of the stars MVlim taking into account the maximum visual absorption (AVmax) at that distance inside the sky area of our survey. MVlim is deﬁned by:

MVlim = Vlim − AVmax(3kpc) − 5log(3kpc) + 5 (9.1)

Fig.9.5 shows the visual absorption AV versus heliocentric distance for the diﬀerent samples deﬁned in Table 9.2. The physical interpretation of the distribution of extinction in distance will 140 CHAPTER 9. STELLAR CONTENT IN THE ANTICENTER

0.4 0.4

0.3 0.3

0.2 0.2

0.1 0.1

S1 inner S1 outer 0.0 0.0 11 12 13 14 15 16 17 18 11 12 13 14 15 16 17 18 V magnitude V magnitude

Figure 9.3: Completeness computed as the ratio between the V magnitude distribution of the complete control sample and the S1 samples (see Table 9.2). In blue, MB samples. In green, EC samples. Left plot shows inner samples, while right plot shows the outer.

1.0 1.0

0.8 0.8

0.6 0.6

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0.2 0.2 S2/S1 inner S2/S1 outer

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1.0 1.0

0.8 0.8

0.6 0.6

0.4 0.4

0.2 0.2 CS/S1 inner CS/S1 outer

0.0 0.0 11 12 13 14 15 16 17 11 12 13 14 15 16 17 V magnitude V magnitude

Figure 9.4: Completeness computed as the ratio between the V magnitude distribution of the S1sampleandtheS2andCSsamples.Inblue,MBandCSsamples.Ingreen,ECsamples. Left plots show inner sky area samples, while right plots show the outer. 9.3. LOOKING FOR A POPULATION COMPLETE UP TO 3 KPC 141

Table 9.2: AV , Vlim,andMVlim for all samples at the bright (min) and faint (max) ends. Spectral type according to the MVlim are shown. N is the number of stars for the absolute magnitude limited samples, i.e. MVlim(1.2 kpc)

MVlim(1.2kpc) [-0.9,0.2] [-1.2,0.0] SPmin [B4-B8.5] [B3.5-B8]

MVlim(3kpc) 1.2 1.2 0.8 0.2 0.2 -0.2 1.1 1.1 0.7 0.1 0.1 -0.3 SPmax A1 A1 A0 B8.5 B8.5 B7.5 A0 A0 B9.5 B8.5 B8.5 B7 N(MVlim) 2209 1565 672 1587 935 278 821 653 361 446 289 133 N (1.2-3kpc) 851 733 349 403 326 106 441 378 185 151 111 33 N/NS1 1.00 0.86 0.65 1.00 0.81 0.63 1.00 0.86 0.82 1.00 0.74 0.57

MVlim(3kpc) 2.1 2.1 1.7 1.1 1.1 0.7 2.0 2.0 1.6 1.0 1.0 0.6 SPmax A6 A6 A4 A0 A0 B9.5 A6 A6 A3 A0 A0 B9.5 N(MVlim) 3647 2771 1561 3329 2292 989 2220 1918 1342 1341 950 521 N (1.2-3kpc) 1883 1622 975 1342 1105 502 1493 1351 926 694 534 260 N/NS1 1.00 0.86 0.69 1.00 0.82 0.59 1.00 0.90 0.80 1.00 0.77 0.73

be analyzed in detail in Chapter 11. As can be seen, the dispersion in AV at a ﬁxed distance is large, mostly due to the clumpy structure of the ISM in the galactic plane. To take this eﬀect into account and to ensure distance completeness of our working samples, we can use not the median AV but a higher value computed like the median plus the standard deviation:

AVmax(r)=AV (r)+σAV (r). The values obtained for AVmax at 3 kpc are in Table 9.2, where we take into account two diﬀerent options: AVmax(r)=AV (r)+σAV (r) and a less restrictive AVmax(r)=AV (r).

Once we have set the Vlim and the AVmax(3kpc) we can compute the MVlim from Eq.9.1. In Fig.9.6 we can see the relation between the distance and the observed limiting apparent magnitude V for diﬀerent MV .TheMVlim values for our samples can be found in Table 9.2. Those absolute magnitudes can be associated to a spectral type assuming they are main sequence (See Annex B). On the other hand, we also computed the most bright absolute magnitude limit taking into account the visual magnitude for which we start suﬀering from saturation, and also the minimum absorption at 1200 pc. Following Table 9.2 we have checked that, when adopting the restriction − AV 1σAV , the completeness limit to be imposed to MV due to saturation is too severe. By taking the stellar volume density from the Besan¸con Galaxy Model, we deduce that there should be ∼65 stars in the range B5-B9 (MV =[-0.84,0.5]) at distances between 1.2 and 1.5 kpc inside 142 CHAPTER 9. STELLAR CONTENT IN THE ANTICENTER

Figure 9.5: AV vs. distance distribution for the MB (left) and EC (right) samples. Blue lines show the moving medians. Black lines enclose the points deviating less than one standard deviation and grey lines the error of the medians. Top black line is he AVmax(r). 9.3. LOOKING FOR A POPULATION COMPLETE UP TO 3 KPC 143

Figure 9.6: Apparent V limiting magnitude as a function of distance for diﬀerent absolute visual magnitudes. AVmax(r)=AV (r)+σ(r) (see Fig.9.5) is taken from MB-S1 sample. Vertical black line shows the 3 kpc limit imposed for our study of the Perseus arm. Horizontal solid line shows the Vlim=16.7 (limit for inner MB-S1 and MB-S2 samples) and Vlim=15.7 (limit for outer MB-S1 and MB-S2 samples). 144 CHAPTER 9. STELLAR CONTENT IN THE ANTICENTER a solid angle of 16 square degrees (our sky area). We took into account the values provided by Robin & Creze (1986) for the solar neighbourhood, the exponential scale length of the galaxy with hR=2500pc and our observed area. On the other hand we checked that the number of stars in our MB-S1 sample within 1200

The spiral arm overdensity

In this Chapter we derive the stellar surface radial proﬁle towards the anticenter. That will allow us both, to analyze the radial scale length of the young population and to quantify the stellar overdensity due to the Perseus spiral arm. In Sect.10.1 we describe the statistical tools that have been implemented for a robust treatment of the samples described in Chapter 9. Results are presented considering both MB and EC methods for the computation of stellar distances. We have the stars radially distributed in the direction of the anticenter. We decided to work with discrete histograms. Diﬀerent methods to obtain the optimal bin width for these histograms will be discussed in Sect. 10.1.1, knowing that it is one of the critical points of the study. Then the surface corrected histograms have been computed as discussed in the following sections.

10.1 Methodology

10.1.1 Derivation of the optimal bin width

The width of the bins have to be small enough to detect the major features of the data we are looking for, but large enough to avoid random ﬂuctuations. In order to optimize the bin size, we analyze three diﬀerent methods:

• Scott (1979)

• Freedman & Diaconis (1981)

• Knuth (2006)

• Scargle et al. (2013)

According to Scott (1979), we assume that our data represent a true underlying density f(x), and it can be represented by a histogram model h(x). Scott (1979) provide formulas that minimize the integrated mean squared error of the histogram model of the true underlying density, i.e.:

L(h(x),f(x)) = (h(x) − f(x))2 (10.1)

145 146 CHAPTER 10. THE SPIRAL ARM OVERDENSITY

Several methods propose optimal bin widths proportional to some estimate of the distribution’s scale, and decreasing with the sample size. For example, Scott (1979) suggested a bin width −1/3 of Δscott =3.49 · σ · N ,beingN the number of points in the data, assuming gaussian distribution and with a variance σ. This rule minimizes the mean integrated square error, but assumes that the underlying distribution is Gaussian, and this is clearly not the case for our density distribution in the anticenter. Freedman & Diaconis (1981) suggested a different rule −1/3 to generalize it to non-Gaussian distributions: ΔF reedman =2(q75 − q25)N ,wherethescale of the distribution is estimated by using the interquartile range. However this method cannot distinguish between unimodal and multimodal distributions with the same scale. This is an important drawback when applying it to our distribution to the anticenter. Knuth (2006) shows that the best piecewise constant model has the number of bins M which maximizes the following function: M 1 M M 1 F (M|{x },I)=N log M+log Γ −M log Γ −log Γ N + + log Γ n + i 2 2 2 k 2 k=1 (10.2) where Γ is the gamma function, nk is the number of measurements xi,locatedinbink. I is the a priory information. The bin width is constant and the number of bins is resulting from the model selection. The method is not only useful to find the optimal bin size, but in addition, it is optimized to find substructure in the data. It gives M=1 for uniform distributions and larger number of bins for a multimodal distribution than for a unimodal distribution even when both samples have the same size. It is also important to mention that Knuth derivation assumes that the uncertainty for each data point is negligible, which is not our case. All the previous methods assumed constant bin width, but Scargle et al. (2013) generalize the Knuth’s model allowing a variable bin width. It uses a Bayesian analysis based on Possionian statistics. All these methods are implemented in AstroML (Vanderplas et al. 2012) packages tools for python. All methods have been checked. Scott (1979) and Freedman & Diaconis (1981) methods are not optimal, as have been already discussed. The tests developed using Scargle et al. (2013) have been proved to be not useful, since very few bins were set in the range [1.2,3] kpc. So we will adopt the Knuth method from now on. In some cases we will compare the results derived from this method with those coming from a simple histogram with a fixed bin size of 200 pc.

10.1.2 Computation of the stellar volume density

In order to obtain the volume stellar density for each of the bins of the histogram we divided the total number of measurements which are included in bin k (k =1,2,3...,nk) denoted as nk, by the total volume of the bin, obtaining a star density value:

− 3 − 3 1 nk Ωobs4π(ρk,max ρk,min) D(ρk)= = nk (10.3) Vk 3 · Ωt

◦ with Ωobs being the solid angle of the observed sky area, inner (∼ 8 ) or inner plus outer ◦ (∼ 16 ). ρk,min and ρk,max are the distance limits of the bin and ρk =(ρk,min + ρk,max)/2, ◦ with Ωt=41252.96 . The√ error bars√ are computed by error propagation of the original error for the number of counts nk,so nk/Vk. 10.1. METHODOLOGY 147

Equation 10.3 assumes that the volume stellar density is constant all inside the volume element considered, that is all inside the truncated cone between (ρk,max,ρk,min). Thus, this correction is no taking into account the vertical density proﬁle of the Galactic disk. Although this approach could be acceptable for nearby regions, where the distance to the plane reached by our stars is small, it is not for more distance bins, that are covering larger distances to the plane where the density is much lower. The possible bias at large distances shall be estimated when analyzing the results. At the largest distance considered for the ﬁtting, i.e. r=3 kpc, the outer sky area of our survey reaches almost b =2◦,so∼100 pc in the direction perpendicular to the plane. This value is of the same order of magnitude of the vertical scale length of our young star population, assumed to be in the range 50-200 pc for stars from B5 to A0 respectively. It means that, for the worst case scenario (B5-type stars), the expected decrease of the volume density at z=100 pc is estimated to be in a factor ∼7(∼ e(100/50)). This bias has been corrected in Sect.10.1.3 when computing the stellar surface density as a function of distance.

10.1.3 Computation of the stellar surface density

The surface density for each bin k can be computed as:

nk Σ(ρk)= (10.4) Sk · Fk where nk is the number of stars in a given radial bin k. Sk is the disk projected surface for that bin, computed from the galactic latitude l covered, the mean distance to the Sun ρk of the bin and the width size of the bin in parsecs. The Fk factor should take into account the quotient between the number of stars included in the galactic latitude interval [bmin,bmax] (computed like zmax,k = ρk · tan(bmax)andzmin,k = ρk · tan(bmin)), and the number of stars expected when integrating all along the vertical direction. To do that we need to assume a vertical distribution 2 of stars, i.e., sech (z/hz), with hz being the scale height of the disk. As known, the vertical scale length (hz) depends on the age of the star, and the values provided by different references have a large uncertainty. Reed (2000) give hz =25-65 pc for OB-type stars (mainly O-B2), while Ma´ız-Apellániz (2001) obtained hz=34.2±0.8±2.5 pc for a sample of O-B5 stars. And Kong & Zhu (2008) using Hipparcos data, obtained hz=103.1±3.0 pc also for OB stars. No values are provided for A type stars, although Czekaj et al. (2013) use 130 pc for stars with ages younger than 0.15 Gyr, and 260 pc for stars with ages between 0.15 and 1 Gyr. So due to the large uncertainty in this data, we decided to apply three different models for a lineal dependence of hz(MV )=Az · MV + Bz, as can be seen in Table 10.1. The different models will directly affect the Fk values, now re-named FZ,i since it depends on the hz parameter and it is different for each star. With the new factor, we are applying a different constant at the final surface density values, and this is affecting directly the Σ values obtained. There is an important degeneracy between the scale height hz imposed and the surface density Σ obtained that our data cannot break. Larger values of hz correspond to larger values of the final obtained surface density Σ as we will see in Sect.10.2.

Due to the dependence hz(MV ), the correction factor need to be computed for each of the stars (i=1,...,nk) in the bin, so the Eq.10.4 have to be modiﬁed as:

n 1 k 1 Σ(ρ )= (10.5) k S F k i=1 Z,i 148 CHAPTER 10. THE SPIRAL ARM OVERDENSITY

Table 10.1: Models for the relation between scale height and the MV of each star. Parameters for the hz(MV )=A · MV + B relation, and obtained hz values for B5 and A5 stars are shown. Az Bz hz(B5) hz(A5) Model A 25.7 71.6 50 pc 120 pc Model B 36.8 130.9 100 pc 200 pc Model C 47.8 170.2 130 pc 260 pc

Figure 10.1: scheme of the distribution of the limits in a bin, with bmin,bmax,zW ,etc.

where FZ,i is the new correction factor for each star, computed as: z − z (ρ) zmax sech2 W dz zmin hz(MV,i) FZ,i(ρ)= − (10.6) +∞ 2 z zW (ρ) −∞ sech dz hz(MV,i) where we also take into account the position of the warp. As have been discussed in Chapter 2 the line of nodes of the galactic warp points very close to the anticenter direction. From ◦ ◦ observational data (2MASS and HI data) Momany et al. (2006) obtained bW ∼-0.5 at l = 180 (see Fig. 10 in Momany et al. (2006)). So we can assume, that at diﬀerent distances, the zW , where the star density of the disk is maximum, can be computed as zW = ρ · tan bW .InFig. 10.1 we can see an scheme of the distribution. In Table 10.2 we can see some FZ values for few example cases. We see how the hz variations give large changes in FZ while the bW parameter almost do not modify the results. √ nk The error in surface density as computed in Eq.10.4 is σΣ(ρk) = . And when computing √Sk · Fk n it using Eq.10.5, the error can be expressed like σ = k . Σ(ρk) · nk (Sk i=1 FZ,i/nk) We expect the Sun to be above the plane of the galaxy: z =26±3pcaccordingtoMajaess et al. (2009) or z =15 pc as adopted in Robin et al. (2003). We have checked that, since all our coordinates are referenced to the Sun, the eﬀect of this value is negligible. 10.1. METHODOLOGY 149

Table 10.2: Correction factors (Fz) for different cases at distances of 1, 2 and 3 kpc. Examples ◦ ◦ ◦ for inner and all sky areas are shown. Three different warp angle values: bW =-0.5 ,0.0 and 0.5 with the corresponding zW values in parsecs. Three different spectral types: B5(MV =-0.84), A0(MV =1.11), and B5(MV 1.88) with the corresponding hz values computed through model A (hz(pc)=25.7 · MV +71.6). ρ=1 kpc ρ=2 kpc ρ=3 kpc B5 A0 A5 B5 A0 A5 B5 A0 A5 bW zW 50pc 100pc 120pc zW 50pc 100pc 120pc zW 50pc 100pc 120pc in -0.5 -9 0.405 0.211 0.177 -17 0.696 0.404 0.343 -26 0.858 0.567 0.490 in 0.0 0 0.396 0.210 0.176 0 0.658 0.395 0.338 0 0.803 0.544 0.475 in +0.5 9 0.368 0.205 0.174 17 0.546 0.368 0.320 26 0.623 0.476 0.429 all -0.5 -9 0.578 0.318 0.268 -17 0.866 0.577 0.500 -26 0.962 0.756 0.677 all 0.0 0 0.571 0.316 0.267 0 0.849 0.570 0.495 0 0.949 0.742 0.666 all +0.5 9 0.541 0.311 0.264 17 0.778 0.540 0.475 26 0.883 0.685 0.622

Table 10.3: Stellar luminosity function Φ(MV ) from Murray et al. (1997) (M97), Jahreiß & Wielen (1997)(JW97), Kroupa (2001)(K01) and Reid et al. (2002)(R02) in units of 10−4 stars per cubic parsec. MV -3.5 -2.5 -1.5 -0.5 0.5 1.5 2.5 3.5 4.5 5.5 6.5 7.5 8.5 9.5 M97 0.02 0.00 0.02 0.23 0.74 1.88 9.58 19.08 23.81 23.71 33.12 17.78 20.02 68.57 JW97 - - 0.30 1.19 3.28 4.77 12.24 17.01 29.24 29.84 29.24 33.42 41.78 70.13 K01 - - 0.15 0.92 2.40 4.10 11.00 15.90 29.20 29.80 29.20 33.40 41.80 70.00 R02 - - - 0.46 0.92 2.60 5.65 13.45 25.36 25.36 32.54 25.52 40.16 58.26

10.1.4 External observational constrains

There are several parameters involved in the analysis for which independent estimations can be collected from the literature. We have used this information both to constrain our ﬁttings and to compare with the obtained results. The radial scale length of the disk has been fully discussed in Sect.2.2. Here we detailed the latest results obtained for the volume density and the surface density in the solar neighborhood.

Volume density in the solar neighbourhood

The volume stellar density at the solar neighbourhood, i.e. the local luminosity function, has been derived by several authors like Murray et al. (1997), Jahreiß & Wielen (1997), Kroupa (2001), and Reid et al. (2002) (see Table 10.3). They provide a resolution of one magnitude, so it will be difficult to reproduce the local star densities for all the working samples with high accuracy. However we can compute the expected number of stars in the solar position for the magnitude ranges (-1.5,1.5), (-1.5,0.5) and (-1.5,-0.5), as can be seen in Table 10.4. The values are pretty different when we use different references, but we will use Kroupa (2001) for next checks of the surface density, since it is the second more recent one, and Reid et al. (2002) only provide values with MV >-0.5. 150 CHAPTER 10. THE SPIRAL ARM OVERDENSITY

Table 10.4: Stellar density at the solar position ρ for diﬀerent absolute magnitudes ranges computed from Murray et al. (1997) (M97), Jahreiß & Wielen (1997)(JW97), Kroupa (2001)(K01) and Reid et al. (2002)(R02) in 10−4 */pc3. Errors are shown when available. MV M97 JW97 K01 R02 (-1.5,1.5) 0.99±0.21 4.77±1.79 3.47±0.13 1.38 (-1.5,0.5) 0.25±0.09 1.49±0.9 1.07±0.53 0.46 (-1.5,-0.5) 0.02±0.02 0.3±0.3 0.15±0.15 -

Table 10.5: Local surface density Σ for diﬀerent hz values and diﬀerent absolute magnitude ranges. The values have been computed from Eq.10.7 and volume density from Kroupa (2001). hz(pc) MV =(-1.5,1.5) MV =(-1.5,0.5) MV =(-1.5,-0.5) 125 0.087±0.028 0.027±0.013 0.004±0.004 200 0.139±0.045 0.043±0.021 0.006±0.006 280 0.194±0.063 0.060±0.030 0.008±0.008

Surface density in the solar neighbourhood

Since we want to study the surface density in the anticenter, we need to transform the local volume density in surface density. To do that we need to assume a vertical density proﬁle ρ(z) 2 and a vertical scale height. Assuming ρ(z)=ρ0 · sech (z/hz), we can compute the local surface density like: ∞ ∞ 2 z Σ = ρ(z)dz = ρsech dz =2ρhz (10.7) −∞ −∞ hz

So using the values in Table 10.4 as a solar density values ρ we can compute the surface density at the sun position Σ just by assuming a scale height for the disk. As discussed, this hz value depends on the spectral type or age of the stars. According Robin & Creze (1986), we have hz=125 pc for logAge=8.4, hz=200 pc for logAge=9 and hz=280 pc for logAge=9.3. So with all these values, we can compute the surface density at the sun position using different parameters, as can be seen in Table 10.5. We see the large range of variations for all these values. In addition, it will be very difficult to reproduce the expected values for our samples, since the ranges of MV for our samples are small, and the available ranges in the literature have not enough accuracy in MV . To solve that, we use a simulation obtained using the Besan¸con Galaxy Model (BGM) to estimate the local surface density. We use the new model (Czekaj et al. 2013) to reproduce a local cylinder of 100 pc of radius. This new approach of the model allows to fix the Initial Mass Function (IMF) and the Star Formation History (SFH). We have used the set of parameters that, according to the authors, provide the best fit to the full sky Tycho data, that is an IMF resulting from the combination of Kroupa (2008) and Haywood et al. (1997) IMFs and a decreasing exponential SFH from Aumer & Binney (2009) (see Czekaj et al. (2013), model B). There are 1 478 545 stars in the simulated sample (Czekaj et al., private communication), 344 696 of them (23%) being the primary of a binary system. By counting the number of stars included in the cylinder and dividing by the surface of the cylinder (S=π · 1002) we can obtain the surface density for different type stars. In Table 10.6 we can see the Hess diagram (i.e. the surface density for each 2D bin in a HR diagram) for the simulated stars. In total, the 2 surface density for the stars with Teff >7000K is 0.176 /pc . Note that the minimum value 10.2. RADIAL DISTRIBUTION 151

2 Table 10.6: Surface density in stars/pc for each 2D bin (MV and Teff ) obtained from the BGM simulation (Czekaj et al., private communication). MV /Teff 30000 20000 15000 12000 10000 9000 8000 7000 -3.5 -3.0 0.32·10−4 -3.0 -2.5 0.32·10−4 0.64·10−4 0.32·10−4 -2.5 -2.0 0.32·10−4 -2.0 -1.5 0.64·10−4 0.64·10−4 0.95·10−4 -1.5 -1.0 0.64·10−4 0.22·10−3 0.64·10−4 0.64·10−4 -1.0 -0.5 0.22·10−3 0.32·10−3 0.29·10−3 0.19·10−3 0.95·10−4 -0.5 0.0 0.16·10−3 0.86·10−3 0.73·10−3 0.45·10−3 0.64·10−3 0.32·10−4 0.0 0.5 0.11·10−2 0.16·10−2 0.92·10−3 0.11·10−2 0.86·10−3 0.5 1.0 0.38·10−3 0.39·10−2 0.24·10−2 0.25·10−2 0.24·10−2 1.0 1.5 0.34·10−2 0.65·10−2 0.62·10−2 0.54·10−2 1.5 2.0 0.35·10−3 0.51·10−2 0.14·10−1 0.14·10−1 2.0 2.5 0.16·10−3 0.12·10−1 0.35·10−1 2.5 3.0 0.16·10−3 0.45·10−1 3.0 3.5 0.71·10−2 -3.5 3.5 0.96·10−4 0.60·10−3 0.30·10−2 0.10·10−1 0.16·10−1 0.37·10−1 0.11·10−0 is 0.34·10−4, i.e., only one star in the simulation belongs this bin, and all the other values are multiples of this one. The advantage of using this simulation to compute the surface density at the Sun’s position is that we can compute the value using the exact ranges of absolute magnitudes that we are using for our samples. In Table 10.7 we can see the values obtained for each sample, taking into account the MVmin and MVmax for each of them.

Other references available are Reed (2000) that gives a value for ΣOB in the range of 6- 80·10−5 /pc2 that agree with the BGM values in Table 10.6. Ma´ız-Apell´aniz (2001) provides −3 2 Σ =(1.62 ± 0.4 ± 0.14) · 10 /pc for O-B5 stars.

10.2 Radial distribution

In Chapter 9 we described our working samples, and in Sect.10.1.3 the method used to compute the surface density for each of them. Here we fit an exponential function at the radial distribution of the surface density. The Perseus overdensity shall be detected as a departure from the fit. The plots and results for all the combination of samples, binning strategies and fitting procedures can be found in Appendix C. Here we analyze in more detail two of them: MB-S1in and CS-MBin, both with the more restrictive AVmax, and with the two bin sizes strategies, 200 pc and the obtained from Knuth method (discussed in Sect.10.1.1):

• MB-S1in: -MB: physical parameters computed using the MB method. -S1: the young star catalog without additional cleaning (see ﬁg.9.1). -inner sky area: the deeper sample (i.e. fainter magnitude) distance complete up to 152 CHAPTER 10. THE SPIRAL ARM OVERDENSITY

Table 10.7: Surface density expected at the Sun’s position for each of our working samples (see Table 9.2). Values derived from Table 10.6. AVmax=2.2-2.3 AVmax=3.1-3.2 2 2 sample MVmin MVmax Σ(/pc ) MVmax Σ(/pc ) MB-S1in -0.9 1.2 0.029 2.1 0.084 MB-S2in -0.9 1.2 0.029 2.1 0.084 CS-MBin -0.9 0.8 0.016 1.7 0.054 EC-S1in -1.2 1.1 0.025 2.0 0.077 EC-S2in -1.2 1.1 0.025 2.0 0.077 CS-ECin -1.2 0.7 0.014 1.6 0.049 MB-S1all -0.9 0.2 0.006 1.1 0.025 MB-S2all -0.9 0.2 0.006 1.1 0.025 CS-MBall -0.9 -0.2 0.002 0.7 0.013 EC-S1all -1.2 0.1 0.005 1.0 0.021 EC-S2all -1.2 0.1 0.005 1.0 0.021 CS-ECall -1.2 -0.3 0.002 0.6 0.011

3kpc.

-restrictive AVmax: To allow us to be completely sure that we are distance complete up to 3 kpc (see Table.9.2).

• CS-MBin: -MB: physical parameters computed using the MB method. -CS: the subset of the young star population with the best physical parameters. -inner sky area: like for MB-S1in.

-restrictive AVmax: like for MB-S1in.

10.2.1 Degeneracy hz − Σ

As discussed in Sect.10.1.3 and 10.1.4, both the vertical scale-height hz and the local surface density Σ are parameters that have large uncertainties. The hz value has been used to compute the surface density for all the histograms (see Eq.10.6), so it affects directly the value of the obtained Σ. Here we have a degeneracy that our data cannot solve. However, not all the combinations of values are possible. To show that, in Fig.10.2 we have fitted an exponential function fixing the local surface density. The radial scale length hR for different scale height models hz(MV ) (see Table 10.1) and fixing three values as zero point Σ, are shown. We see that not all the combinations fit well. As expected, small values of hz are needed when small values of Σ are fixed. When we try to impose small values of hz with large values of Σ we see clearly that the fit to our data show large departures from the model and the fitting line do not follow the points at large distances. From previous sections, and although we are aware of the uncertainties in hz and Σ, we can state that the more acceptable values from recent literature are those of the model B (i.e. hz =100 pc for B5 stars and hz =200 pc for B5 stars) since they fit better with the values of Σ derived from the BGM simulations. Assuming these values, 10.2. RADIAL DISTRIBUTION 153

hz =50-120pc hz =100-200pc hz =130-260 0.010 0.016 0.020 h =3500 ±400 0.014 R h =5800 ±1600 0.008 hR =1800 ±100 R 0.012 0.015 0.006 0.010 BGM

Σ 0.008 0.010 0.004 0.6 0.006

0.004 0.005 0.002 0.002

0.000 0.000 0.000 0.010 0.016 0.020 h =1800 ±100 0.014 R h =2400 ±200 0.008 R 0.012 hR =1190 ±70 0.015 0.006 0.010 BGM

Σ 0.008 0.010 0.004 1.0 0.006

0.004 0.005 0.002 0.002

0.000 0.000 0.000 0.010 0.016 0.020 h =1360 ±70 0.014 R h =1680 ±90 0.008 R 0.012 hR =900 ±60 0.015 0.006 0.010 BGM

Σ 0.008 0.010 0.004 1.4 0.006

0.004 0.005 0.002 0.002

0.000 0.000 0.000 500 1000 1500 2000 2500 3000 3500 4000 500 1000 1500 2000 2500 3000 3500 4000 500 1000 1500 2000 2500 3000 3500 4000 distance (pc) distance (pc) distance (pc)

Figure 10.2: Star surface density for the MB-S1in sample in blue. Solid blue line show the points between 1.2 and 3 kpc used for the exponential fit. Vertical red lines show the 1.2 and 3 kpc completeness limits. Three different hz models have been imposed. Exponential fit is plotted in pink, with the obtained hR parameter in pc. Three different local surface density values are used as a zero point: the ΣBGM =0.029 provided by BGM in middle panels (see Table 10.7), 0.6·ΣBGM in top panels, and 1.4·ΣBGM bottom panels.

we obtain hR=1.8±1.0 kpc, and a clear inconsistency between the model and data centered at ∼1.7 kpc from the Sun, the ﬁrst indicator of a stellar overdensity induced by the Perseus arm.

10.2.2 Radial scale length

Figure 10.3 shows the exponential fit to the surface density distribution obtained from the MB- S1in and CS-MBin samples. All the fits for the other samples can be seen in AnnexC. Table 10.8 shows the same results. Again we clearly see a peak in the distribution around 1.7 kpc. In previous section we only fitted the hR, but now both hR and Σ have been treated as free parameters. For MB-S1in there are two points above the fit, while for CS-MBin we can only detect one. Then there is an underdensity and a possible second peak around 2.5 kpc.

We observe that, although changing the binning method, the model for the hz or the considered sample, the values derived for the radial scale length of our young population are all cases in the range [1.6,2.2] kpc. At this point it is important to have in mind that this parameter have been obtained considering all the points inside the range [1.2,3.0] kpc. So, if the stellar overdensity induced by the Perseus arm observed in Fig.10.3 is real, we shall perform a new ﬁt avoiding the points around the position of the peak. Thus, we repeat the ﬁts rejecting those points located in the Perseus arm region, i.e. between 1400 and 2000 pc. The results can be seen in Fig.10.4 and in Table 10.9. We can see that the scale length slightly increased a bit when we rejected the points around the the arm region. 154 CHAPTER 10. THE SPIRAL ARM OVERDENSITY

hz =50-120pc hz =100-200pc hz =130-260pc 0.010 0.016 0.020 h =2000 ±500 h =2000 ±500 R h =2200 ±600 0.014 R Σ =0.034 ±.008 0.008 R Σ =0.026 ±.006 0.012 0.015 Σ =0.014 ±.003 0.006 0.010 0.008 0.010 0.004 0.006 0.004 0.005 0.002 MBS1in 0.002 MBS1in MBS1in 0.000 0.000 0.000 0.010 0.016 0.020 h =1700 ±300 h =1700 ±300 R h =1900 ±300 0.014 R Σ =0.041 ±.007 0.008 R Σ =0.032 ±.005 0.012 0.015 Σ =0.017 ±0.003 0.006 0.010 0.008 0.010 0.004 0.006 0.004 0.005 0.002 MBS1in 0.002 MBS1in MBS1in 0.000 0.000 0.000

2 0.0035 h =2000 ±500 h =1900 ±500 hR =2200 ±600 0.006 R R 0.008 Σ =0.013 ±0.003 0.0030 Σ =0.005 ±0.001 Σ =0.010 ±0.002 0.005 0.0025 0.004 0.006

stars/pc 0.0020 0.003 0.0015 0.004 0.0010 0.002 CSMBin 0.002 0.0005 CSMBin 0.001 CSMBin 0.0000 0.000 0.000 0.0035 h =1700 ±300 h =1600 ±300 hR =1800 ±300 0.006 R R 0.008 Σ =0.017 ±0.003 0.0030 Σ =0.007 ±0.001 Σ =0.013 ±0.002 0.005 0.0025 0.004 0.006 0.0020 0.003 0.0015 0.004 0.0010 0.002 CSMBin 0.002 0.0005 CSMBin 0.001 CSMBin 0.0000 0.000 0.000 500 1000 1500 2000 2500 3000 3500 4000 500 1000 1500 2000 2500 3000 3500 4000 500 1000 1500 2000 2500 3000 3500 4000 distance (pc) distance (pc) distance (pc)

Figure 10.3: Radial variation of the star surface density for the MB-S1in and CS-MBin samples in blue. Solid blue line show the points between 1.2 and 3 kpc used for the fit. Vertical red lines show the 1.2 and 3 kpc completeness limits. Three different hz models have been used. The exponential fit is plotted in pink, with the obtained hR and Σ parameters are expressed in pc and /pc2 respectively. First row is for the MB-S1in sample, Knuth bin size. Second row is for the MB-S1in sample, 200 pc bin size. Third row is for the CS-MBin sample, Knuth bin size. Fourth row is for the CS-MBin sample, 200 pc bin size.

Table 10.8: Radial scale length (in pc) and local surface density (in /pc2) derived from the exponential ﬁt obtained using all the data between 1.2 and 3 kpc. hz=50-120pc hz=100-200pc hz=130-260pc Sample bin size hR Σ hR Σ hR Σ MB-S1in Knuth 2200± 600 0.014±0.003 2000± 500 0.026±0.006 2000± 500 0.034±0.008 MB-S1in 200pc 1900± 300 0.017±0.003 1700± 300 0.032±0.005 1700± 300 0.041±0.007 CS-MBin Knuth 2200± 600 0.005±0.001 2000± 500 0.010±0.002 1900± 500 0.013±0.003 CS-MBin 200pc 1800± 300 0.007±0.001 1700± 300 0.013±0.002 1600± 300 0.017±0.003 10.3. THE PERSEUS ARM OVERDENSITY 155

Table 10.9: Radial scale length (in pc) and local surface density (in /pc2) derived from the exponential ﬁt obtained when the points in the region [1.4,2.0] kpc are avoided. hz=50-120pc hz=100-200pc hz=130-260pc Sample bin size hR Σ hR Σ hR Σ MB-S1in Knuth 2900± 500 0.010±0.001 2600± 400 0.019±0.002 2500± 400 0.024±0.003 MB-S1in 200pc 2200± 400 0.014±0.002 2000± 300 0.025±0.004 2000± 300 0.033±0.005 CS-MBin Knuth 2500± 800 0.004±0.001 2200± 600 0.008±0.002 2200± 500 0.011±0.003 CS-MBin 200pc 2000± 300 0.006±0.001 1800± 200 0.011±0.001 1700± 200 0.015±0.002

Thus, we state that the best fitted value for hR is in the range [1.7,2.9] kpc. And taking into account that the CS-MBin sample has less stars (maybe too few stars for a robust statistical treatment) and that the most probable values for hz are in the range hz = 100 − 200 pc (model B), we obtain a radial scale length for the young stars of hR ∼ [2.0,2.6] kpc. Sale et al. (2010) derived the stellar density profile of young stars in the anticenter using IPHAS data. By selecting A-type stars they derived an inner and outer radial scale length for the thin disk of ∼3.0 kpc and 1.2 kpc. See this compilation of recent derivation of this parameter in their paper. Only one radial exponential scale length has been fitted here, as our sample can be assumed complete only up to 3 kpc from the Sun, that is about 12 kpc from the Galactic center. Our results are between the two hR values obtained by Sale et al. (2010), getting closer to the value of the inner scale length.

The fitted zero points Σ, as discussed, depend on the hz(MV ) model imposed, increasing for larger hz values. We have also seen that results from model B (hz =100-200 pc for B5-A5) fit better with the surface density values derived from BGM (see Sect.10.2.1). As expected, the Σ obtained are larger for the MB-S1in sample (since it includes B4-A1 stars) than for the CS-MBin sample (including B4-A0 stars). The expected values for these parameters, as obtained from the BGM can be seen in Table 10.7. The values derived for MB-S1in sample using model B 2 2 for the hz (0.019 /pc and 0.025 /pc , see Table 10.9) have the same order than the expected value 0.029 /pc2 (see Table 10.7). On the other hand, the values obtained for the CS-MBin 2 2 (0.008 /pc and 0.011 /pc ) have to be corrected for the factor N/NS1 =0.65 defined in Table 9.2, that takes into account the fraction of stars rejected due to the cleaning process of the sample. Then, the resulting values 0.012 /pc2 and 0.017 /pc2 are well in agreement with the expected 0.016 /pc2 value.

10.3 The Perseus arm overdensity

We develop χ2 tests for the different fits performed in previous sections to quantitatively evaluate obs the significance of the Perseus arm overdensity. The number of stars observed (nk ,with k =1,m) for all the m bins between 1.2 and 3 kpc is compared with the distribution coming from the exponential fit. As a first approximation, to compare model and observations, we have fit 2 used the value at the at the middle distance of each bin (nk ). The χ value have been computed as: 2 m nobs − nfit 2 k k χ = fit (10.8) k=1 nk 156 CHAPTER 10. THE SPIRAL ARM OVERDENSITY

hz =50-120pc hz =100-200pc hz =130-260pc 0.010 0.016 0.020 h =2500 ± 400 h =2600 ± 400 R h =2900 ± 500 0.014 R Σ =0.024 ±0.003 0.008 R Σ =0.019 ±0.002 0.012 0.015 Σ =0.010 ±0.001 0.006 0.010 0.008 0.010 0.004 0.006 0.004 0.005 0.002 MBS1in 0.002 MBS1in MBS1in 0.000 0.000 0.000 0.010 0.016 0.020 h =2000 ± 300 h =2000 ± 300 R h =2200 ± 400 0.014 R Σ =0.033 ±0.005 0.008 R Σ =0.025 ±0.004 0.012 0.015 Σ =0.014 ±0.002 0.006 0.010 0.008 0.010 0.004 0.006 0.004 0.005 0.002 MBS1in 0.002 MBS1in MBS1in 0.000 0.000 0.000

2 0.0035 h =2200 ± 600 h =2200 ± 500 hR =2500 ± 800 0.006 R R 0.008 Σ =0.011 ±0.003 0.0030 Σ =0.004 ±0.001 Σ =0.008 ±0.002 0.005 0.0025 0.004 0.006

stars/pc 0.0020 0.003 0.0015 0.004 0.0010 0.002 CSMBin 0.002 0.0005 CSMBin 0.001 CSMBin 0.0000 0.000 0.000 0.0035 h =1800 ± 200 h =1700 ± 200 hR =2000 ± 300 0.006 R R 0.008 Σ =0.015 ±0.002 0.0030 Σ =0.006 ±0.001 Σ =0.011 ±0.001 0.005 0.0025 0.004 0.006 0.0020 0.003 0.0015 0.004 0.0010 0.002 CSMBin 0.002 0.0005 CSMBin 0.001 CSMBin 0.0000 0.000 0.000 500 1000 1500 2000 2500 3000 3500 4000 500 1000 1500 2000 2500 3000 3500 4000 500 1000 1500 2000 2500 3000 3500 4000 distance (pc) distance (pc) distance (pc)

Figure 10.4: Star surface density for the MB-S1in and CS-MBin samples in blue. Vertical red lines show the 1.2 and 3 kpc completeness limits. Three different hz models have been used. Only green points have been used for the fit, avoiding the arm. Exponential fit is plotted in 2 pink, with the obtained hR and Σ parameters in pc and /pc respectively. First row is for the MB-S1in sample, Knuth bin size. Second row is for the MB-S1in sample, 200 pc bin size. Third row is for the CS-MBin sample, Knuth bin size. Fourth row is for the CS-MBin sample, 200 pc bin size. 10.3. THE PERSEUS ARM OVERDENSITY 157

Table 10.10: Probability value obtained from a χ2 test for the S1 and CS samples, and for MB and EC methods for the distance derivation. Restrictive version of AVmax have been used. Model B for the scale height is adopted (hz=100-200 pc for B5-A5). Fits for all the points between 1.2 and 3 kpc (fit with arm, FWA in the table) and fits without the points between 1.4 and 2 kpc (fit without arm, FWOA in the table) have been considered. N is the number of stars between 1.2 and 3 kpc used for the test. MB EC bin N f.w.a. f.w.o.a. N f.w.a. f.w.o.a. S1 in knuth 852 5% 0.1% 822 7% 8% S1 in 200pc 852 11% 4% 822 7% 10% CS in knuth 350 17% 2% 186 - - CS in 200pc 350 30% 46% 186 - -

Table 10.11: Significance of the detection of the Perseus arm obtained from the number of stars in the peak bins and those expected from the fit. Values for the S1 and MB samples, restrictive version of AVmax have been used. Model B for the scale height (hz = 100 − 200 pc) is adopted. Fits for all the points between 1.2 and 3 kpc (fit with arm, FWA in the table) and fits without the points between 1.5 and 2 kpc (fit without arm, FWOA in the table) have been considered. MB EC bin FWA FWOA FWA FWOA S1 in knuth 1.8 3.4 0 -0.2 S1 in 200pc 1.0 2.4 -0.6 0.4 CS in knuth 0.9 2.2 - - CS in 200pc -0.4 0.7 - -

fit where nk have been computed from the surface density obtained from the fitted expression fit fit fit · · Σk , and transformed to the number of stars per bin using: nk =Σk Sk FZ,i . FZ,i is the average of FZ,i for all the stars in the bin previously used to transform from observed nk to observed surface density Σ(ρk) (see Sect.10.1.3). Then, considering the degrees of freedom for 2 each histogram (i.e. number of bins minus three, since hR,Σ and χ have been estimated), the probability factor is obtained, giving the probability of observing a test statistic at least as extreme as the χ2 obtained, and indicating whether we can reject our hypothesis that the data is coming from an exponential distribution. We show in Table 10.10 the results for S1 and CS samples, for the inner sky area, and the two methods to derive distances (MB and EC). Model B for the scale height (hz=100-200 pc for B5-A5) is used. Being the null hypothesis that the distribution comes from a simple exponential, we see in Table 10.10 how most of the results deviate from it, i.e. most of the distributions do not agree with an exponential. In fact, using the optimal binning (i.e. Knuth) a pure exponential density distribution can be rejected at 5% level of significance for MB method. The other models have either too few stars or distances from the EC method. This deviation is clearly coming from the overdensity due to the Perseus arm. One would expect that the fit without arm has smaller values of the probability (i.e. the deviation from the null hypothesis should be larger), since we rejected the points close to the arm for the fit but not for the χ2 computation. We see that this is true for most of the samples, like the MB-S1in sample with knuth bin size, decreasing the probability from 5% to 0.1%. We can understand these tendencies by looking at figures 10.3 and 158 CHAPTER 10. THE SPIRAL ARM OVERDENSITY

10.4 (fits for the EC samples can be found in appendix C). Fits for CS-EC do not give coherent results, since there are too few stars in each bin, so they are not statistically robust. √ We can estimate the significance of the peak like (narm − nfit)/ narm,wherenarm is the number of stars in the bins close to the arm (i.e. between 1.4 and 3.0 kpc), and nfit is the expected number of stars from the exponential fit (when we do not use the arm bins for this fit) in this same region. We can see these values in Table 10.11. We see that for the EC samples the peak is not significant, but for the MB method, and the S1 sample (having more stars than CS), the significance is clear, specially when the fit has been developed without taking into account the arm bins. In this case (MB-S1 sample, inner region, and knuth bin size) we obtain narm=296 stars, and nfit=237 stars. Thus we obtain a value of 3.4, i.e. more than 3σ of significance. The amplitude of the arm can also be estimated like (narm − nfit)/(narm + nfit) obtaining in this case a ∼10% amplitude for the overdensity associated to the Perseus arm. Chapter 11

The spiral arm dust layer

The individual distances and visual absorptions for thousands of stars obtained in this work allow us to create a 3D extinction map in the anticenter direction. Two sets of physical parameters are available, those of MB and EC methods. The absorptions given by the two methods are very similar, with systematics smaller than 0.05mag (see Fig.8.14). The diﬀerences in distances are small, although they can reach 20%, presenting signiﬁcant trends. The EC distances can be ∼200 pc smaller than MB distances at ∼1700 pc, the position of the spiral arm estimated in previous sections. Since the resulting absorption map will be very similar for both methods we will only analyze here those obtained using the MB method, and more precisely the MB-S1.dat sample (so, once we rejected the emission line and the cold stars, see Fig.9.1) that will provide more stars, and so, more statistics to compute the 3D map. The map can be computed until large distances, although for more distant regions, the number of stars available will be smaller, and the error in distances larger, so the resolution achieved will be worse. For that matter, and since we want to study here the region around the Perseus spiral arm (∼1500-2000 pc), we only analyze the 3D map until 4000 pc.

11.1 Extinction map in the anticenter

A grid in the anticenter is created, and the individual visual absorptions AV are combined in order to compute the mean absorption at each point of the grid. The absorption AV at each point of the grid has been computed using all the available stars of the sample weighted by the gaussian of the distance to the grid, that is: − 2 N Δri AV exp 2 i=1 i 2σ AV = − 2 (11.1) N Δri i=1 exp 2σ2 where N is the total number of stars in the sample and Δri is the distance between the ith star and the point of the grid. The value of σ is the radius used for the gaussian weight, and it is diﬀerent at diﬀerent regions of the grid. For points of the grid closer to the Sun, the star density will be larger, and we can use smaller sigma values. But for further points, due to the fact that we are working with a V magnitude limited sample (and not the one complete in distance) and

159 160 CHAPTER 11. THE SPIRAL ARM DUST LAYER

100

Nσ=5

80 Nσ=10

Nσ=20

60 (pc) σ

0 500 1000 1500 2000 2500 3000 3500 4000 distance (pc)

Figure 11.1: σ(Nσ) values as a function of distance for Nσ=5 (blue),Nσ=10 (green) and Nσ=20 (red). Dispersion due to the different σ values are also shown by the thinner lines. also due to the scale length of the galaxy, the star density will be lower. Then we will have to smooth over a larger volume, since every point of the grid will have less stars around. To compute the σ for each point of the grid, first we compute the distance between the point and each star of the grid. Then we choose as σ, the distance to the Nσth star closer to the point. So the point of the grid will always have Nσ stars closer than 1σ. Values like Nσ=5, 10, 20 have been checked. The σ(Nσ) obtained in each case, as a function of distance, can be found in Fig.11.1. We use Nσ=5 since it gives larger resolution. However it may also include some noise features. The steps at which the mean absorption is computed are 2.5 in galactic longitude and latitude and 20 pc in distance. This method allows to obtain a smooth grid that will be more detailed in closer regions where we have more information, and average over large regions when the information available is smaller. We have to point out that this method can include some bias at the edge of the grids, where the information available is not complete: these points only have stars in one direction, so the final AV will be biased trough the AV present in the inner parts of the sky area. Figure 11.3 shows the visual absorption in a (l, b) distribution map for six different distances. We can study there the different features that appear in the map. On the other hand, we show in Fig.11.2 the 2D extinction map projected on the galactic (x, y)and(x, z) planes where we averaged all the stars at different z and y by using the same Eq.11.1 but for the 2-dimensional case. (x, y, z) are the cartesian galactic heliocentric coordinates.

11.2 Froebrich extinction map

The extinction map provided by Froebrich et al. (2007) based on 2MASS data can be compared with the data derived from our survey. First we can compare it with our map of the star density per square degree obtained (see Fig.11.4), computed as the star counts in 0.1deg radius from each point. A clear correlation is evident in the sense that low extinction regions have the larger stellar density. There we have to take into account that the limiting magnitude in our ﬁeld is not constant (see Fig.4.6). However, the main features are perfectly reproduced by the two maps. Second, the Froebrich et al. (2007) map can be compared with our maps in Fig.11.3, although here we have to remember that Froebrich only provide the line of sight column density of dust, 11.2. FROEBRICH EXTINCTION MAP 161

Figure 11.2: Top: 2D extinction map in (x, y), where stars for all z have been used Bottom:: 2D extinction map in (x, z), where stars for all y have been used. AV is color-coded. 162 CHAPTER 11. THE SPIRAL ARM DUST LAYER

Figure 11.3: 2D extinction maps in (l,b) at six diﬀerent distances from the Sun, 1000, 1500, 2000, 2500 and 3000 pc. AV is color-coded, with a shift of 0.2 mag in the color scale between consecutive plots. A larger resolution version of this plot can be found in http://www.am.ub.edu/ mmonguio/FIGURES/Av3D1.eps 11.3. THE PERSEUS DUST LAYER 163

Figure 11.4: left) Number of stars per square degree in our survey area computed using the number of stars within a radius of 0.1deg (full sample of 35974 stars with complete uvbyHβ data). right) AV extinction map based on color excess maps from 2MASS and provided by Froebrich et al. (2007). i.e. extinction, whereas we present a full 3D map for this region. Again, the irregularities observed in both maps are well correlated.

11.3 The Perseus dust layer

Figure 11.6-left shows the absorption as a function of distance for nine different (l,b) directions. For most of the regions there is a clear change of slope around 1.7 kpc that matches with the location of the Perseus arm. To see it more clearly, we also plotted the first derivative of the absorption as a function of the distance in Fig.11.6-right, where the two step distribution is clear. We would expect, for constant absorption, a flat distribution of the dAV /dr. The presence of a cloud would translate to a bump in the dAV /dr distribution. And a two step distribution indicates two different dust densities before and after the jump. We can see this two trend distribution clearly in our figures, with the jump located between 1500 and 2000 pc, so just matching with the presence of the arm. This decrease of dAV /dr is present in all the directions. Then, for l = 178◦ we can also find, after 2 kpc, the presence of many other condensations of the interstellar medium (that will be discussed in next section). As described by Puerari & Dottori (1997), the star formation induced by the shock in a stellar density wave scenario produces an azimuthal spread of ages across the spiral arms. At the corotation radius (CR), the angular velocity of the spiral perturbation (Ωp) and that of the stellar disk (Ω) are the same. A comoving observer at the CR will see outward and inward the shock front change from one side of the spiral to the other, consequently reversing the order in which young and older disk stellar populations appear in azimuthal profiles across the arm. We have not analyzed in detail the stellar overdensity distribution as a function of age in our working sample of young stars (this is deserved as a future work). However, if we analyze the dust distribution (i.e. interstellar extinction) along the line of sight, we can use it as an indicator of the dust layer and assume that this dust lane along the stellar arm is the signature of the spiral shock wave (although the strict coincidence of a shock and a lane is not obligatory; Gittins & Clarke (2004)). From that we can use our 3D extinction map to estimate the CR radius in 164 CHAPTER 11. THE SPIRAL ARM DUST LAYER

Figure 11.5: Picture from Puerari & Dottori (1997) the MW galactic disk. Roberts (1972) did a theoretical pioneer work in this research line by discussing the shock formation along the Perseus arm on the basis of the Density-Wave theory of Spiral Structure. A deep discussion on the optical tracers of spiral wave resonances in external galaxies can be found in Elmegreen et al. (1992). Puerari & Dottori (1997) provide a good sketch of the Z-trailing spatial arms conﬁguration expected for the MW (their Fig.1 is reproduced here in Fig.11.5). Figure 11.6-right suggests us that the dust layer is just in front of the Perseus arm so the corotation radius of the spiral pattern (if density wave mechanism is assumed) is further away that the location of Perseus in the anticenter, so at least at RCR > 10.5 kpc. This result is well in agreement with the position of the CR radius suggested by Antoja et al. (2011), who proposed an angular velocity of the perturbation (Ωp) of about 16-20 km/s/kpc so at a galactocentric radius of RCR=11-14 kpc.

11.4 Irregularities in the AV distribution

Figure 11.3 shows the (l,b) extinction maps at six diﬀerent distances. We clearly see some higher extinction regions. At the left part of the plot, around l=178◦ there is a large cloud with a peak at (178.8, -1.3) and ∼2.5 kpc. On the other hand, there are some other features at (l,b)∼(182.4,-0.4) in the 1.5 kpc map and another in (l,b)∼(181.8,0.3) and 2 kpc. The global structure of the interstellar medium observed in Fig.11.3 is well identiﬁed in the extinction maps of Dobashi et al. (2005) (see their Fig.18-5-7 and our Sect.2.4.2). These authors presented both, the 2D extinction maps obtained applying the traditional star-count techniques (with resolution of 6) and a quantitative catalog of dark clouds and clumps observed in our working sky area. According to these authors, no previously known dark clouds were found in our sky area, as we intended when selected our area.

Reipurth & Yan (2008) present the Hα image of the supernova remnant Simieis 147, having 3◦ of diameter. The pulsar PSRJ0538+2817 has been found near its center, with a VLBA +0.42 ∼ distance of 1.47−0.27 kpc. This object is centered at (l,b) (179.7, -1.7), so very close to the edge of our survey. Rodr´ıguez et al. (2006) fond a molecular cloud in the anticenter, associated with the two IRAS 11.4. IRREGULARITIES IN THE AV DISTRIBUTION 165 sources IRAS05431 + 2629 at (l, b)=(182.1,-1.1) and IRAS05490 + 2658 at (l,b)=(182.4,+0.3). This last HII region is also found by Blitz et al. (1982) at (l,b)=(182.36,+0.19) through CO observations, and they state a distance of d=2.1±0.7 kpc. We can see that this region matches with a feature in our d=1500 pc extinction map. We present in figure 11.7 the differential absorption for four of these mentioned directions. For (182.4,-0.4), the feature seen in the 1.5 kpc map, is barely seen here, with a second peak at 2.3 kpc. At (179.7,-1.7), through the direction of the pulsar PSRJ0538+2817 there is a small feature around 1.5 kpc that could match with its location, and a more prominent feature at 3 kpc. For the (182.4,+0.3) direction there is a small bump at 2 kpc but not so clear, since we see the features slightly shifted. This feature can be related with that observed at (181.8 0.3) at 2 kpc. Finally, the feature claimed by Rodr´ıguez et al. (2006) at (182.1,-1.1) is perfectly seen as a peak in our fig.11.7-bottom-right at ∼1.7 kpc, so 400 pc away of the 2.1±0.7 kpc that Blitz et al. (1982) claimed. Their distances have been computed through spectrophotometry of the stars exciting the HII region. Our method allows to compute the distances to the clouds with much more accuracy than they do. 166 CHAPTER 11. THE SPIRAL ARM DUST LAYER

◦ 3.5 l=178 l=178 ◦ 3.0 0.0010 ◦ 2.5 b=-1.75 ◦ 0.0005 2.0 b=-0.75 (mag/pc) (mag)

V ◦

b=0.0 /dr A 1.5 ◦ V 0.0000 b=-1.75 1.0 dA b=-0.75 ◦ b=0.0 ◦ 0.5 −0.0005 0.0 ◦ 3.5 l=180 l=180 ◦ 3.0 0.0010

2.5 0.0005 2.0 (mag/pc) (mag) V /dr A 1.5 ◦ ◦ V 0.0000 b=-1.5

b=-1.5 dA 1.0 b=-0.5 ◦ b=-0.5 ◦ b=0.5 ◦ 0.5 b=0.5 ◦ −0.0005 0.0 500 1000 1500 2000 2500 3000 3500 ◦ 3.5 l=182 l=182 ◦ ◦ 3.0 b=-1.0 0.0010

2.5 0.0005 2.0 (mag/pc) (mag) V /dr A 1.5 ◦ V b=-1.0 ◦ 0.0000 1.0 b=-0.25 dA b=-0.25 ◦ ◦ b=1.0 ◦ 0.5 b=1.0 −0.0005 0.0 500 1000 1500 2000 2500 3000 3500 500 1000 1500 2000 2500 3000 3500 Dist (pc) Dist (pc)

Figure 11.6: Left: Absorption vs. distance for nine diﬀerent (l,b) directions indicated in the plots. Right: Diﬀerential absorption (dAV /dr) of the absorption for the nine mentioned directions, showing the change of slope of the absorption as a function of distance. 11.4. IRREGULARITIES IN THE AV DISTRIBUTION 167

0.0015 (182.4,-0.4) (179.7,-1.7)

0.0010

(mag/pc) 0.0005 /dr V dA

0.0000

0.0015 (182.1,-1.1) (182.4,0.3)

0.0010

(mag/pc) 0.0005 /dr V dA

0.0000

500 1000 1500 2000 2500 3000 3500 500 1000 1500 2000 2500 3000 3500 distance (pc) distance (pc)

Figure 11.7: Diﬀerential absorption dAV /dr as a function of distance for four diﬀerent directions. 168 CHAPTER 11. THE SPIRAL ARM DUST LAYER Chapter 12

Towards the detection of the kinematic perturbation

In previous chapters, we studied the overdensity due to the Perseus arm, as well as the dust layer associated to it. The next step, still under development, is to study the kinematic perturbation due to the arm, through radial velocities from the stars in our sample. Intermediate young stars from our photometric survey have been selected for the spectroscopic survey. The detection of both, a density and velocity perturbation associated to the Perseus will clearly identify it as a major spiral arm. A quantitative estimate of the amplitude of the stellar overdensity and the amplitude of the radial velocity perturbation will be a test of the density wave theory. We need to measure the radial velocity distribution across the arm in order to determine the perturbation. We observe close to the anticenter to minimize the eﬀect of the galactic rotation as mentioned in Chapter 3. The stars we use for this study are old enough to both have a relaxed kinematics and had time to response to the density wave perturbation. On the other hand, they are also young enough to have a relatively small velocity dispersion and thereby a strong response to a potential perturbation. Then, only stars younger than few times 108 years will be useful. This suggests a spectral range of B5-A5, although in the future A5-F0 type stars close to the zero age main sequence could also be selected. Some F-surpegiants detected in our photometric survey can be added to the spectroscopic sample. Those will allow us to go deeper in the galactic disk, up to the Cygnus arm, providing new insights on the disk cut-oﬀ. This part of the project is just starting and all the available data is still being reduced.

12.1 Simulating the expected kinematic perturbation.

Several simulations have been made in order to check the number of stars needed for a signiﬁcant detection of the kinematic signature, considering both the intrinsic motion of our young stars and the observational errors expected from the spectroscopic survey. We modeled the kinematic eﬀect of the spiral arm with a sinusoidal radial velocity perturbation: RV = A(1 − cos(πr/DSP )) where A is the amplitude of the kinematic perturbation, r is the distance between the star and the Sun, and DSP the distance between the Sun and the locus of the Perseus arm. We assume that the Sun is near the interarm region, so the systematic heliocentric velocity of the stars placed at the locus of the Perseus arm would be 2A when looking

169 170CHAPTER 12. TOWARDS THE DETECTION OF THE KINEMATIC PERTURBATION

Figure 12.1: Simulation of the kinematic perturbation due to the spiral arm through a sinusoidal radial velocity function. Dots are the mean velocity for each 0.5kpc distance bin. Error bars show both the error of the mean and five times the error of the mean. Dashed lines show the standard deviation. Left) sinusoidal amplitude A=0km/s (no perturbation). Right) A=5km/s. In both cases a total sample of 750 stars have been considered in the simulation. Observational errors of 5km/s are included in the simulation. from the Sun. We add to this radial velocity perturbation a random distribution assuming our young population has an intrinsic radial velocity dispersion as a function of the spectral type as proposed by Aumer & Binney (2009). We also add an observational Gaussian error in radial velocity of 5km/s. The radial distribution of stars (initial positions for the velocity simulation) is obtained from the real distribution we found from the photometric survey. Once the velocity is computed, we also add a 10% error in distance. The values adopted for the radial amplitude perturbation (A) have been taken from the literature. These values are small, most of them in the range 3-7km/s (Fernández et al. 2001; Mishurov et al. 1997; Mel’Nik et al. 1999; Mishurov & Zenina 1999). In all cases the error bars are very large indicating how difficult has been, up to now, the derivation of this parameter. Fig.12.1 shows an example of the statistics obtained from these simulations. We have undertaken some statistical tests in order to check our capability to detect the arm as a function of the amplitude and the number of stars. From that we concluded that, to reach a 3σ detection (i.e. 99%) of a 2.5km/s amplitude perturbation, we require ∼750 stars in the spectroscopic sample. We should take into account that some of the observed stars will be double stars, so their radial velocity will be affected and they will not be useful for our purposes. The fraction of binary stars has been estimated to be around 30% (Evans et al. 2010) or 60% (Arenou 2011), so we should increase the number of observed stars till ∼1000 stars.In order to identify and reject most of the binaries, at least two different observational periods are needed (see Sana et al. (2009)).

12.2 Observational radial velocity program with WYFFOS@WHT

A pilot survey observational program started at the William Herschel Telescope (WHT) using WYFFOS.The instrument WYFFOS, together with the AutoFib2 robot, is a multi-object fibre 12.3. FIRST ATTEMPT USING LAMOST DATA 171 spectrograph with 150 fibers (16 each) in a 30 radius field. The grating that is being used is H4200B with 0.17 A˚/pix, centered at 4200A˚ with a wavelength coverage of 600A˚. Our observing program include B5-A3 stars with distances up to 2.5 kpc and V ≤17 mag. In total, 12 fields have been observed, at two different epochs each of them. Since around 50 stars can be placed in a fiber for each field, spectra for around 600 stars have been obtained. The data reduction process is still not finished. A new pipeline provided by the WHT staff is being used, but since it was mainly developed using red spectra, we are finding some problems when reducing our blue spectral range.

12.3 First attempt using LAMOST data

The LAMOST pilot survey (see 2.3.3) provides spectra and radial velocity for several thousands of stars. When crossmatching these stars with our complete survey (with 35974 stars) we ﬁnd 1108 stars in common. Figure 12.2 shows the distribution of V , Teff , radial velocity and the corresponding errors for these stars. We see that the observational error obtained in radial velocity is pretty small, with about 50% of the sample with errors smaller than 3km/s. We check their radial velocity distribution as a function of the distance (computed using the MB method, see Chapter 6 for details). When using all the available stars, the distribution has too large dispersion to see anything. On the other hand, when using only hot stars (Teff >7000K), there seems to be a wave feature (see Fig.12.2-bottom-right). However the statistics are still too low, and the results are also consistent with no feature at all. In any case, the results look promising, and the future conﬁrmation of this kinematic perturbation combined with the stellar overdensity estimated in Chapter 10, would allow us to estimate the amplitude of the potential perturbation. 172CHAPTER 12. TOWARDS THE DETECTION OF THE KINEMATIC PERTURBATION

Figure 12.2: Top-left: magnitude distribution for the 1108 stars with both LAMOST and photometric data in our survey. Top-right: eﬀective temperature distribution (from MB method). Middle-top-left: Radial velocity distribution for these stars. Middle-top-right: error in radial velocity provided by LAMOST survey. Middle-bottom-left: Radial velocity distribution for the stars with Teff > 7000K. Middle-bottom-right: error in radial velocity provided by LAMOST survey for the stars with Teff > 7000K. Bottom-left: radial velocity vs. MB distance for all the stars. Bottom-right: radial velocity vs. MB distance for star with Teff > 7000K. Chapter 13

Summary, conclusions and future perspectives

The results of this thesis are very encouraging since they quantify, for the first time, the overdensity of young stars associated to the Perseus spiral arm and the distribution of the interstellar material linked to it. The detection of this dust lane supports the existence of a density wave and, furthermore, its position well in front of the arm, places the corotation radius of the Milky Way spiral pattern more than two kiloparsec away from the Sun’s position in the anticenter direction. Also important, this study presents a significant advance in mapping the outer part of the Perseus arm, thus connecting the arm’s features previously observed in the second and third Galactic quadrant. The work developed here can be summarized in the achievement of three main milestones. First, a Strömgren photometric survey with about one hundred thousand stars (96980 stars with partial data and 35974 with all the indexes) in the anticenter direction has been built and published. Second, we have developed a new tool for the computation of physical parameters for young stars, a tool based on the most recently published atmospheric grids and stellar evolutionary tracks. And third, covering the aims of the project, this information has been used to study the star density distribution in the anticenter direction. Our data also allowed us to create a 3D extinction map linking the dust distribution with the Perseus arm.

13.1 Summary and conclusions

Here we summarize the main outcomes of the whole thesis, and examine perspectives for future studies in the next section.

AnewStr¨omgren photometric survey in the anticenter

A uvbyHβ Str¨omgren photometric survey covering 16 ◦ in the anticenter direction has been carried out using the Wide Field Camera at the Isaac Newton Telescope. This is the natural photometric system for identifying young stars and obtaining accurate estimates of individual distances and ages. The survey is centered slightly below the plane in order to take into account the warp, and covers galactic longitudes from l ∼177◦ to l ∼ 183◦ and galactic latitudes from

173 174 CHAPTER 13. SUMMARY, CONCLUSIONS AND FUTURE PERSPECTIVES b ∼−2◦ to b ∼ 1.5◦. The calibration to the standard system has been undertaken using open clusters. We have created a main catalog of 35974 stars with all Str¨omgren indexes and a more extended one with 96980 stars with partial data. The central 8◦ reach ∼90% completeness at V∼ 17mag, while the outer region of ∼8◦, mostly observed with only one pointing, reaches this completeness at V ∼ 15.5mag. Photo- metric internal precisions between 0.01-0.02mag for stars brighter than V =16whereobtained, increasing to 0.05mag for some indexes and fainter stars (V =18-19). The catalogs with the individual measurements and the ﬁnal mean magnitudes and color indexes are published in electronic form via the CDS.

A tool for the derivation of physical parameters of young stars

Several calibrations were already available from the literature, most of them from the 80’s and based on previous cluster data and trigonometric parallaxes. Here, we have taken advantage of the latest improvements on the stellar atmosphere and stellar evolutionary models to design, implement and test a new tool for physical parameter derivation. The availability of accurate trigonometric parallaxes from Hipparcos has allowed us to perform an exhaustive test for both the classical empirical method (EC) and the new model based method (MB) developed here. Some trends and biases are detailed in Chapter 7. By applying both methods to our survey data we have derived distances, visual absolute magnitudes, visual interstellar absorption and ages for a set of ∼12000 stars with Teff < 7000K. Whereas the empirical method requires a previous classification in photometric regions, the new methods do not, thus they avoid the discontinuities present in the first one. The new method, that only uses the extinction free colour indexes [m1], [c1],Hβ, has been demonstrated to be more powerful for distant stars, when the extinction is important. Furthermore, this methods takes into account the corresponding photometric errors, therefore, it treats more rigorously the faint stars in our survey. The comparison of the obtained distances with Hipparcos data has allowed us to select the optimal atmospheric grids for stars hotter than Teff =7000K. Although this new method brings us several advantages, some ambiguity in the gap region between very early- and late-type stars still remains, basically for faint stars with large photometric errors. We shall emphasize that distances derived using the two methods show a clear bias, that can be estimated to be up to 20% relative error in distance, giving larger distances for the MB method. Although this drawback do not affect the detection of the spiral arm overdensity it would shift the position of the arm. We want to point out that, the statement which is often made in the literature, that relative error in photometric distances are about 10-15%, does not take this systematic biases into account. Another example of that is the clear shift obtained between our distances and those computed from IPHAS data for early-A type stars. Again this bias can reach 10-15% at 2 kpc from the Sun, but now, distances from our new MB method are smaller than the once obtained from IPHAS data. The IPHAS and 2MASS data have helped us to identify and reject emission line stars and to check for wrongly classified stars in the gap region, respectively.

The stellar overdensity and the dust lane associated to Perseus

In Chapter 9 several criteria have been discussed in detail and implemented in order to produce a distance complete sample of young stars with accurate information. Since we need to evaluate 13.1. SUMMARY AND CONCLUSIONS 175 the variation of the star density at different distances, we need to ensure that we have samples complete at a given distance range. We have thoroughly discussed the limiting distance range and the cuts in absolute magnitude needed, due to both, apparent limiting magnitude at the faint end and saturation problems at the bright end. All possible biases have been evaluated and avoided in the final working sample. We have succeeded to produce samples complete in the distance range [1.2,3] kpc, where we expect the overdensity induced by Perseus. With this samples we have proceeded to study the star density distribution as a function of distance. Surface density was chosen to be the best option, since it can take into account the area surveyed, the effect of the scale height of the galaxy, as well as the warp present in that direction. The radial surface density distribution has been checked using the different samples available, as well as using both distance methods. An exponential scale length of the disk has been fitted, considering as free parameters the surface density at the Sun position (Σ)and radial scale length (hR). More homogeneous results are derived from distances computed using the new MB method proposed here. The results obtained for the local surface density depend on the absolute magnitude range selected, as well as on the scale height of the Galaxy assumed to compute the surface density. For example, for the MB-S1 sample, using only the inner region, complete between 1.2 and 3 kpc (i.e. selecting the intrinsic luminosity range of MV =[-0.9,1.2]), and assuming hz = 100pc for B5 stars and hz=200 pc for A5 stars, we obtain a surface density 2 of Σ=0.026±0.006 stars per pc , well in agreement with recent values derived from the new version of the Besan¸con Galaxy Model. Despite the values obtained, the uncertainty for this parameter remains since it is highly correlated with the assumed scale height for the population.

Values derived for the radial scale length of the young population are in the range hR ∼[1.7- 2.0] kpc when we use all the stars between 1.2 and 3 kpc. But they show a clear overdensity at 1.7 kpc, associated with the Perseus arm. So when avoiding those bins close to the arm position (i.e. between 1.4 and 2 kpc), the scale length obtained when fitting the remaining data increases to values in the range hR ∼[2.0-2.6] kpc. The obtained overdensity around 1.7 kpc allow us to reject the null hypothesis of a pure exponential density distribution at a 5% level of significance for those samples with more stars, and using the MB method for physical parameter derivation. In addition, these histograms also show an amplitude of the arm around 10%, with a significance of the peak larger than 3σ,when we take into account the number of stars located around the peak and those expected from the exponential fitting. Our data also allowed us to create a 3D extinction map in our survey area. By studying the absorption AV as a function of distance we find two different slopes, i.e. a two step distribution in its variation dAV /dr. This is coherent with a two different densities of the interstellar medium. This two trend distribution can be seen in different (l, b) directions in our survey, and in all cases the jump appears at 1.7 kpc, just around the Perseus arm position. This fact agrees with a larger density dust layer before the arm, and lower dust density behind it. Following Roberts (1972) models this scenario matches with a dust layer before the arm, indicating that we could be inside the corotation radius and in agreement with the existence of a density wave. Additionally, our 3D reddening map provides the location of different clouds, some of them already identified from the literature. The study of the differential absorption dAV /dr also can detect these clouds, providing accurate distances. 176 CHAPTER 13. SUMMARY, CONCLUSIONS AND FUTURE PERSPECTIVES

13.2 Improvements and future perspectives

The results of this thesis show very important outcomes. However, several improvements are needed in order to definitively estimate the spiral arm amplitude and to disentangle the nature of the spirals and the mechanism that provokes it. We finish with a list of some examples of ongoing and future research lines for this study. (i) Searching for the kinematic signature. The photometric survey presented here has provided a list of targets for the spectroscopic survey. We plan to continue working in the reduction process of the radial velocity pilot survey of young stars carried out using the multifiber spectrograph WYFFOS@WHT. Several hundred spectra have already been obtained and are now being reduced. Before undertaking the full observational programme it is mandatory to deeply analyze the actual accuracy on the radial velocities we can reach for stars at about 2-3 kpc from the Sun. We plan to exploit the on-going releases of the LAMOST survey in the anticenter for our purposes. Both, LAMOST and WYFFOS radial velocities will be compared and their respective internal accuracy tested. In the near future, the most important outcome of Gaia will be a well-defined distance. However, Gaia spectra, due to its wavelength coverage, will be marginal for the quantitative spectroscopic analysis required for our young and hot stars. The WEAVE@WHT multi-object spectrograph, which low (R=5000) and high resolution mode (R=20000), will be ideal for our purposes. This project will definitively test if the Milky Way spiral pattern is compatible with a density wave or if mechanisms like manifolds driven by the galactic bar are also dominant in outer spiral arms. (ii) Detection of age gradients in the Perseus arm. Acceptable good photometric ages are available for the stars of our working samples (see Chapter 9).We wonder if, with an accurate statistical treatment, we can detect the age distribution across the arm, crucial information to unveil the dominant mechanism that drives this structure. Results obtained here could benefit the study of the age gradients being studied in the long term project recently started at the WFC@INT in Canary Islands. (iii) Extending the physical parameter derivation method for cold stars. We plan to extend the MB method developed in this thesis to stars cooler than 7000K. That would optimize not only the distance but also the metallicity determination for these objects. We want to investigate if methods such those recently proposed by Sale (2012), based in hierar- chical Bayesian probability, can be applied to the Strömgren photometry or, even more, si- multaneously to 2MASS, Strömgren and IPHAS data. A simultaneous derivation of the mean distance-extinction relationship would be optimal for the analysis of both Perseus and the outer arms. (iv) Scientific exploitation of the Strömgren Survey. The catalog presented in this thesis has many more applications than those developed in this work. As an example, the detection of F-supergiants present in our sample and its photometric distance derivation can provide us new insights on the truncation process of the thin disk and on the position of the outer Cygnus arm. Having in mind that our survey contains several thousand of F and G type stars with all photometric indexes, we can attempt to analyze the metallicity gradient of the thin disk one or two kpc out of the galactocentric radius. The application of some multivariate data analysis techniques to the 3D stellar distribution in our survey could lead to the detection of new clusters. Good available photometric data for NGC1893 (used as standard field), Teutch 5 and Teutch 10 clusters (included in our survey area), can provide better estimation of their physical parameters. Appendix A

Tables

This appendix includes some tables with detailed information about the catalog and the photometric transformation process. Table A.1 shows the extinction coefficients obtained for each night and filter, as well as the airmass ranges covered by the calibration fields. In Table A.2 we detail the range of magnitudes and color indexes covered by our calibration fields. The coefficients for the transformation to the standard system through Eqs. 4.2 and 4.7 with their associated errors, for each of the observing nights, are shown in Tables A.3 and A.5, respectively. Tables A.6 and A.7 provide the column description for the two catalogs, which are individual measurements and final mean values, respectively. Table A.8 shows, as an example, the ten first rows of the mean catalog. For the individual measurements catalog, the ten first rows are not provided owing to the large amount of data included, but the full table can be found at the CDS.

Table A.1: Extinction coeﬃcients obtained with the WFC/INT at El Roque de los Muchachos. 2009Feb13 2009Feb17 2011Feb08 2011Jan09 2011Jan10 2011Jan11 2011Feb16 2011Feb17 ku 0.553 0.575 0.605 0.574 0.556 0.537 0.550 0.528 kv 0.318 0.380 0.350 0.292 0.324 0.283 0.299 0.298 kb 0.219 0.245 0.261 0.195 0.214 0.174 0.206 0.232 ky 0.183 0.184 0.200 0.120 0.151 0.101 0.131 0.161 kw 0.191 0.213 0.218 0.148 0.174 0.129 0.168 0.163 kn 0.186 0.200 0.173 0.162 0.195 0.154 0.162 0.174 (kw + kn)/2 0.188 0.205 0.195 0.155 0.184 0.141 0.165 0.169 χmin − χmax 1.0 - 1.5 1.0 - 2.1 1.0 - 1.8 1.0 - 1.7 1.0 - 1.8 1.0 - 1.7 1.0 - 1.6 1.0 - 1.7 Notes. Errors are between 0.01 and 0.03 magnitudes per airmass unit. Last row shows the airmass ranges used to derive these coeﬃcients.

Table A.2: Color index photometric ranges for the calibration ﬁelds Field V(b-y)c1 (v-b) m1 Hβ Praesepe 6 - 14 0.0 - 0.6 0.1 - 1.1 0.2 - 1.2 0.1 - 0.6 2.5 - 2.9 NGC1893 13 - 16 0.1 - 1.2 0.05 - 1.25 0.3 - 1.6 -0.15 - 0.7 2.4 - 3.0 Coma 5 - 11 0.1 - 1.1 0.2 - 1.1 0.2 - 1.6 0.1 - 0.6 2.5 - 2.9 ac308 13 - 16 0.25 - 1.6 0.03 - 1.3 0.4 - 1.6 -0.2 - 0.7 2.5 - 3.0 ac406 13.5 - 16.5 0.2 - 1.4 0.1 - 1.3 0.4 - 1.6 -0.1 - 0.7 2.5 - 3.0

177 178 APPENDIX A. TABLES

Table A.3: Standard transformation coeﬃcients. Equation 4.2 Equation 4.3 Equation 4.4 chip A1 B1 A2 C2 A3 B3 C3 2009 Feb 13 1 -24.909±0.001 -0.073±0.002 -0.225±0.001 0.975±0.003 -0.323±0.006 -0.072±0.008 0.950±0.004 2 -24.704±0.001 -0.056±0.002 -0.266±0.001 0.967±0.002 -0.332±0.005 -0.126±0.006 0.975±0.004 3 -24.853±0.001 -0.073±0.002 -0.238±0.001 0.989±0.002 0.013±0.004 -0.103±0.005 0.954±0.004 4 -24.796±0.001 -0.078±0.001 -0.217±0.001 0.971±0.002 -0.177±0.004 -0.079±0.006 0.982±0.003 2009 Feb 16 1 -24.827±0.001 -0.067±0.002 -0.244±0.002 0.974±0.003 -0.241±0.005 -0.153±0.006 0.971±0.005 2 -24.626±0.002 -0.050±0.003 -0.289±0.002 0.982±0.003 -0.229±0.007 -0.210±0.008 0.960±0.006 3 -24.767±0.002 -0.087±0.003 -0.247±0.002 0.981±0.003 0.094±0.007 -0.118±0.008 0.982±0.006 4 -24.718±0.002 -0.069±0.003 -0.248±0.002 0.985±0.003 -0.075±0.008 -0.132±0.010 0.961±0.006 2011 Jan 08 1 -24.807±0.001 -0.068±0.002 -0.216±0.002 0.968±0.002 -0.304±0.005 -0.147±0.006 0.977±0.005 2 -24.591±0.001 -0.054±0.002 -0.264±0.002 0.991±0.003 -0.311±0.005 -0.144±0.006 0.966±0.005 3 -24.696±0.001 -0.087±0.002 -0.210±0.002 0.983±0.003 -0.017±0.006 -0.128±0.007 0.974±0.005 4 -24.693±0.002 -0.073±0.003 -0.224±0.002 0.988±0.004 -0.161±0.008 -0.115±0.010 0.948±0.006 2011 Jan 09 1 -24.735±0.005 -0.069±0.012 -0.231±0.005 0.970±0.013 -0.322±0.012 -0.139±0.028 0.985±0.013 2 -24.514±0.005 -0.053±0.013 -0.281±0.005 0.988±0.013 -0.328±0.015 -0.167±0.034 0.971±0.015 3 -24.621±0.010 -0.087±0.025 -0.232±0.008 0.980±0.019 -0.036±0.011 -0.112±0.025 0.973±0.012 4 -24.618±0.005 -0.072±0.013 -0.243±0.005 0.990±0.013 -0.190±0.013 -0.122±0.030 0.956±0.014 2011 Jan 10 1 -24.749±0.007 -0.109±0.019 -0.216±0.009 0.956±0.022 -0.231±0.019 -0.139±0.045 0.964±0.020 2 -24.532±0.008 -0.077±0.020 -0.265±0.006 0.970±0.015 -0.254±0.019 -0.149±0.043 0.974±0.020 3 -24.646±0.008 -0.074±0.020 -0.237±0.009 0.985±0.024 0.055±0.014 -0.141±0.033 0.960±0.015 4 -24.638±0.009 -0.087±0.022 -0.229±0.007 0.971±0.016 -0.133±0.024 -0.032±0.051 0.926±0.023 2011 Jan 11 1 -24.715±0.002 -0.062±0.004 -0.234±0.002 0.974±0.004 -0.260±0.006 -0.148±0.008 0.973±0.007 2 -24.494±0.003 -0.047±0.004 -0.282±0.003 0.988±0.004 -0.339±0.007 -0.176±0.010 0.969±0.005 3 -24.597±0.002 -0.072±0.004 -0.238±0.002 0.984±0.004 0.030±0.006 -0.132±0.009 0.961±0.006 4 -24.598±0.003 -0.063±0.005 -0.231±0.002 0.978±0.004 -0.138±0.007 -0.087±0.009 0.933±0.005 2011 Feb 16 1 -24.745±0.004 -0.080±0.008 -0.233±0.007 0.973±0.013 -0.325±0.016 -0.087±0.026 0.971±0.015 2 -24.519±0.004 -0.059±0.006 -0.282±0.005 0.964±0.009 -0.299±0.018 -0.144±0.025 0.933±0.011 3 -24.624±0.003 -0.081±0.005 -0.258±0.005 1.003±0.008 -0.023±0.014 -0.100±0.021 0.960±0.011 4 -24.633±0.004 -0.063±0.007 -0.248±0.006 0.992±0.012 -0.210±0.019 -0.052±0.030 0.955±0.013 2011 Feb 17 1 -24.761±0.004 -0.097±0.006 -0.214±0.004 0.956±0.007 -0.293±0.010 -0.157±0.014 0.983±0.011 2 -24.546±0.004 -0.058±0.006 -0.282±0.005 0.949±0.009 -0.307±0.015 -0.174±0.020 0.954±0.009 3 -24.663±0.003 -0.078±0.005 -0.240±0.004 0.980±0.007 -0.005±0.013 -0.147±0.017 0.940±0.010 4 -24.665±0.003 -0.069±0.006 -0.236±0.004 0.990±0.007 -0.171±0.014 -0.112±0.021 0.948±0.011 179

Table A.4: Standard transformation coeﬃcients (continuation). Equation 4.5 Equation 4.6 chip A4 B4 C4 D4 A5 B5 C5 2009 Feb 13 1 0.169±0.003 0.152±0.009 0.969±0.007 0.028±0.003 2.330±0.002 -0.034±0.003 0.843±0.004 2 0.226±0.003 0.263±0.007 0.940±0.006 0.013±0.002 2.328±0.001 -0.046±0.003 0.873±0.004 3 0.285±0.002 0.197±0.006 0.957±0.004 0.017±0.002 2.343±0.001 -0.047±0.002 0.901±0.004 4 0.343±0.002 0.298±0.006 0.892±0.005 0.015±0.002 2.332±0.001 -0.045±0.002 0.857±0.003 2009 Feb 16 1 0.133±0.005 0.220±0.010 0.918±0.009 0.001±0.005 2.332±0.001 -0.047±0.002 0.856±0.004 2 0.167±0.004 0.287±0.009 0.931±0.008 0.024±0.004 2.320±0.002 -0.080±0.003 0.844±0.005 3 0.238±0.004 0.205±0.010 0.943±0.008 0.014±0.004 2.350±0.002 -0.036±0.003 1.003±0.005 4 0.292±0.004 0.266±0.009 0.946±0.007 0.016±0.003 2.322±0.002 -0.044±0.004 0.843±0.005 2011 Jan 08 1 0.181±0.003 0.201±0.005 0.940±0.005 0.010±0.003 2.330±0.001 -0.043±0.002 0.866±0.005 2 0.219±0.003 0.236±0.006 0.957±0.005 0.033±0.003 2.324±0.002 -0.064±0.003 0.875±0.005 3 0.281±0.003 0.200±0.006 0.952±0.005 0.023±0.003 2.323±0.002 -0.042±0.003 0.998±0.006 4 0.335±0.003 0.246±0.007 0.965±0.005 0.021±0.002 2.306±0.002 -0.039±0.004 0.847±0.005 2011 Jan 09 1 0.165±0.005 0.192±0.025 0.951±0.021 0.011±0.005 2.324±0.007 -0.048±0.017 0.860±0.025 2 0.210±0.006 0.240±0.029 0.955±0.024 0.029±0.006 2.322±0.007 -0.067±0.018 0.882±0.026 3 0.269±0.005 0.203±0.025 0.951±0.020 0.026±0.005 2.326±0.006 -0.036±0.016 1.015±0.026 4 0.328±0.006 0.234±0.029 0.972±0.023 0.019±0.006 2.303±0.007 -0.037±0.018 0.854±0.027 2011 Jan 10 1 0.161±0.006 0.181±0.027 0.966±0.025 0.013±0.006 2.313±0.010 -0.027±0.027 0.828±0.037 2 0.190±0.009 0.170±0.042 1.036±0.033 0.012±0.010 2.327±0.008 -0.009±0.020 0.953±0.032 3 0.273±0.008 0.166±0.036 0.975±0.026 0.013±0.008 2.323±0.011 -0.057±0.028 0.905±0.041 4 0.342±0.006 0.135±0.027 1.022±0.019 0.011±0.006 2.299±0.012 -0.018±0.031 0.815±0.041 2011 Jan 11 1 0.165±0.004 0.188±0.008 0.945±0.007 0.002±0.004 2.340±0.003 -0.053±0.005 0.837±0.009 2 0.199±0.004 0.212±0.008 0.979±0.007 0.017±0.003 2.340±0.003 -0.071±0.005 0.886±0.007 3 0.265±0.003 0.213±0.007 0.939±0.006 0.019±0.003 2.338±0.003 -0.057±0.005 0.959±0.008 4 0.327±0.003 0.213±0.008 0.971±0.007 0.015±0.003 2.314±0.003 -0.045±0.005 0.828±0.007 2011 Feb 16 1 0.189±0.009 0.129±0.023 0.981±0.017 0.014±0.009 2.307±0.007 -0.024±0.013 0.831±0.018 2 0.228±0.010 0.203±0.023 0.972±0.020 0.027±0.007 2.314±0.006 -0.046±0.011 0.883±0.012 3 0.291±0.007 0.175±0.020 0.957±0.017 0.021±0.006 2.323±0.005 -0.053±0.009 0.950±0.013 4 0.354±0.010 0.152±0.026 1.010±0.023 0.018±0.007 2.293±0.007 -0.040±0.014 0.823±0.013 2011 Feb 17 1 0.206±0.006 0.173±0.014 0.966±0.011 0.018±0.007 2.294±0.004 -0.049±0.007 0.849±0.011 2 0.259±0.009 0.300±0.018 0.912±0.015 0.021±0.006 2.303±0.004 -0.054±0.008 0.871±0.008 3 0.320±0.006 0.183±0.014 0.973±0.011 0.027±0.005 2.311±0.004 -0.056±0.007 0.936±0.009 4 0.386±0.009 0.173±0.018 1.005±0.018 0.015±0.007 2.275±0.005 -0.027±0.008 0.846±0.010 180 APPENDIX A. TABLES

Table A.5: Standard transformation coeﬃcients for Eqs. 4.7 chip Equation 4.7 Equation 4.8 A˜4 B˜4 C˜4 A˜5 C˜5 2009 Feb 13 1 0.195±0.002 0.165±0.009 0.940±0.007 2.315±0.001 0.865±0.004 2 0.237±0.002 0.269±0.007 0.929±0.005 2.308±0.001 0.911±0.004 3 0.300±0.001 0.185±0.006 0.956±0.004 2.325±0.001 0.957±0.004 4 0.356±0.001 0.290±0.006 0.891±0.005 2.315±0.001 0.896±0.003 2009 Feb 16 1 0.135±0.003 0.222±0.010 0.917±0.008 2.306±0.001 0.882±0.005 2 0.185±0.003 0.312±0.008 0.903±0.007 2.272±0.001 0.877±0.008 3 0.252±0.003 0.213±0.009 0.930±0.008 2.332±0.001 1.033±0.005 4 0.308±0.003 0.266±0.010 0.935±0.007 2.299±0.001 0.867±0.005 2011 Jan 08 1 0.189±0.002 0.208±0.005 0.931±0.004 2.292±0.002 0.886±0.011 2 0.245±0.002 0.264±0.006 0.922±0.005 2.277±0.001 0.903±0.010 3 0.303±0.002 0.212±0.006 0.929±0.005 2.295±0.001 1.029±0.009 4 0.356±0.002 0.253±0.007 0.946±0.005 2.272±0.002 0.872±0.011 2011 Jan 09 1 0.178±0.002 0.174±0.007 0.969±0.005 2.302±0.001 0.891±0.004 2 0.225±0.002 0.262±0.009 0.941±0.007 2.297±0.001 0.937±0.007 3 0.292±0.002 0.185±0.008 0.960±0.006 2.302±0.001 0.979±0.005 4 0.348±0.002 0.229±0.008 0.946±0.006 2.290±0.001 0.899±0.004 2011 Jan 10 1 0.172±0.002 0.189±0.006 0.948±0.005 2.308±0.001 0.882±0.004 2 0.216±0.002 0.232±0.006 0.950±0.004 2.306±0.001 0.919±0.005 3 0.283±0.002 0.196±0.006 0.946±0.005 2.306±0.001 0.978±0.004 4 0.341±0.002 0.253±0.007 0.923±0.005 2.293±0.001 0.874±0.004 2011 Jan 11 1 0.166±0.002 0.189±0.007 0.943±0.006 2.312±0.002 0.854±0.010 2 0.215±0.003 0.224±0.008 0.961±0.006 2.302±0.001 0.913±0.009 3 0.281±0.002 0.225±0.007 0.921±0.005 2.308±0.001 0.983±0.009 4 0.341±0.002 0.223±0.008 0.954±0.006 2.292±0.001 0.849±0.007 2011 Feb 16 1 0.198±0.007 0.138±0.022 0.969±0.016 2.295±0.003 0.841±0.017 2 0.256±0.007 0.235±0.023 0.926±0.017 2.289±0.002 0.903±0.011 3 0.308±0.006 0.197±0.020 0.931±0.015 2.296±0.002 0.967±0.013 4 0.372±0.007 0.174±0.025 0.978±0.020 2.274±0.002 0.839±0.012 2011 Feb 17 1 0.216±0.005 0.182±0.013 0.955±0.010 2.282±0.002 0.861±0.012 2 0.281±0.006 0.319±0.018 0.883±0.012 2.285±0.001 0.890±0.008 3 0.343±0.005 0.203±0.014 0.946±0.010 2.293±0.001 0.957±0.010 4 0.400±0.006 0.187±0.018 0.982±0.015 2.274±0.002 0.856±0.010 181

Table A.6: Readme file of the catalog with individual measurements Column Label Units Explanation 1 RAdeg deg Right ascension J2000.0 2eRAdeg arcsec Internal error of RAdeg 3 DEdeg deg Declination J2000.0 4eDEdeg arcsec Internal error of DEdeg 5 Vmag mag Magnitude transformed to the standard Johnson V magnitude 6eVmag mag Error of Vmag 7(b-y)magStrömgren (b-y) color index 8e(b-y) mag Error of (b-y) 9c1magStrömgren c1 index 10 e c1 mag Error of c1 11 (v-b) mag Strömgren (v-b) color index 12 e (v-b) mag Error of (v-b) 13 m1 mag Strömgren m1 index 14 e m1 mag Error of m1 15 Hbeta mag Strömgren Hβ index 16 e Hbeta mag Error of Hbeta 17 RAdegu deg Right ascension J2000.0 in the u filter CCD image 18 DEdegu deg Declination J2000.0 in the u filter CCD image 19 umag mag Instrumental u magnitude 20 e umag mag Error of umag 21 umagEC mag Instrumental u magnitude extinction corrected 22 e umagEC mag Error of umagEC 23 AMu – Air mass for umag 24 Xu pixels X pixel position for umag 25 Yu pixels Y pixel position for umag 26 texpu sec Exposure time for umag 27 radu pixels Radius used to derive umag from aperture photometry 28 skyu counts Sky counts associated to umag 29 sdskyu counts Standard deviation on skyu 30 JDu days Julian Date for umag 31 umagco mag Raw instrumental u magnitude from IRAF daofind 32 idmagu – ID number in the u magnitude file 33-48 Same as Columns 17-32 for v magnitude 49-64 Same as Columns 17-32 for b magnitude 65-80 Same as Columns 17-32 for y magnitude 81-96 Same as Columns 17-32 for Hβw magnitude 97-112 Same as Columns 17-32 for Hβn magnitude 113 file – Name of the file where the photometry comes from (contains information on chip number, field number, and pointing) 114 ichip – WFC chip number 115 flagFA – Flag indicating which of the six filters (u, v, b, y, Hβw,Hβn) are available 116 ID – Identifier of the star which the measure belongs to 117 XmN – Number of measurements with the same ID 182 APPENDIX A. TABLES

Table A.7: Readme file for the catalog with mean measurements Column Label Units Description 1IDIDnumber 2 RAdeg deg Right ascension J2000.0 3eRAdeg arcsec Internal mean error of RAdeg 4oRAdeg – Number of measurements for RAdeg 5 DEdeg deg Declination J2000.0 6eDEdeg arcsec Internal mean error of DEdeg 7oDEdeg – Number of measurements for DEdeg 8 Vmag mag Mean magnitude transformed to the standard Johnson V magnitude 9eVmag mag Error of Vmag (error of the mean for o Vmag≥2 and internal standard deviation for o Vmag=1) 10 o Vmag – Number of measurements for Vmag 11 (b-y) mag Mean Strömgren (b-y) color index 12 e (b-y) mag Error of (b-y) 13 o (b-y) – Number of measurements for (b-y) 14 c1 mag Mean Strömgren c1 index 15 e c1 mag Error of c1 16 o c1 – Number of measurements for c1 17 (v-b) mag Mean Strömgren (v-b) color index 18 e (v-b) mag Error of (v-b) 19 o (v-b) – Number of measurements for (v-b) 20 m1 mag Mean Strömgren m1 index 21 e m1 mag Error of m1 22 o m1 – Number of measurements for m1 23 Hbeta mag Mean Strömgren Hβ index 24 e Hbeta mag Error of Hbeta 25 o Hbeta – Number of measurements for Hbeta 26 meanJD days Mean Julian Date 27 flagIA – Flag indicating which of the six indexes (V,(b − y),c1,m1, (v − b),Hβ) are available 28 flagTS – Flag indicating how many measures for each index are inconsistent according to a Student’s t-test 29 GSC2 – GSC2 identifier 183

Table A.8: Example of the first ten rows of the catalog with mean measurements (see Table A.7) ID RAdeg e RAdeg o RAdeg DEdeg e DEdeg o DEdeg Vmag e Vmag o Vmag 1 83.7644656 0.025 4 30.1846810 0.018 2 11.836 0.048 4 2 83.7602742 0.020 3 30.0734584 0.011 1 14.088 0.328 2 3 83.7323671 0.010 3 30.2406015 0.019 4 14.081 0.046 4 4 83.7099509 0.162 4 30.1193681 0.131 3 14.325 0.056 3 5 83.7027602 0.140 4 30.1502936 0.001 2 13.543 0.045 4 6 83.7020158 0.002 2 30.1233125 0.061 2 14.272 0.025 1 7 83.6966936 0.243 2 30.1856348 0.018 2 14.797 0.026 1 8 83.6437971 0.175 3 30.1128599 0.001 2 12.742 0.078 3 9 83.6371473 0.029 3 30.0746250 0.053 3 13.914 0.041 3 10 83.6125620 0.032 3 30.0857448 0.014 3 13.706 0.064 3 (b-y) e (b-y) o (b-y) c1 e c1 o c1 (v-b) e (v-b) o (v-b) 0.327 0.177 4 1.014 0.022 3 0.446 0.006 3 0.455 0.354 2 1.043 0.043 2 0.643 0.187 2 0.495 0.007 4 0.638 0.023 3 0.695 0.008 3 0.502 0.008 3 0.813 0.003 3 0.597 0.009 3 0.938 0.010 4 0.376 0.022 4 1.073 0.012 4 0.750 0.050 1 0.316 0.075 1 0.933 0.057 1 0.387 0.053 1 1.009 0.083 1 0.541 0.059 1 1.019 0.014 3 0.468 0.041 3 1.232 0.023 3 0.662 0.012 3 0.453 0.014 3 0.710 0.015 3 0.562 0.010 3 0.962 0.009 3 0.575 0.007 3 m1 e m1 o m1 Hbeta e Hbeta o Hbeta 0.044 0.397 4 2.924 0.018 4 0.166 0.574 2 2.975 0.055 4 0.200 0.015 3 2.806 0.008 4 0.095 0.017 3 2.851 0.010 3 0.134 0.021 4 2.640 0.000 2 0.183 0.076 1 2.630 0.017 1 0.154 0.079 1 2.979 0.034 1 0.213 0.037 3 2.647 0.003 2 0.049 0.027 3 2.682 0.003 3 0.013 0.017 3 2.832 0.012 3 meanJD flagIA flagTS GSC2 2455582.5239636 111111 00010010 N9UG000329 2455582.5239636 111111 00110110 N9UG000390 2455582.5239636 111111 00000000 N9UG000301 2455582.5239636 111111 00000000 N9UG000367 2455582.5239636 111111 10000000 N9UG000351 2455591.5528230 111111 01000000 N9UG000365 2455591.5536240 111111 10000000 N9UG015193 2455585.5365401 111111 00000000 N9UG000370 2455585.5365401 111111 00000000 N9UG000387 2455585.5365401 111111 00000000 N9UG000383 184 APPENDIX A. TABLES 0.009 0.009 0.007 0.005 0.006 0.006 0.005 0.004 0.005 0.006 0.012 0.014 0.012 0.013 0.004 0.004 0.005 0.006 0.004 0.005 0.012 0.009 0.011 0.012 0.009 0.007 0.009 0.008 0.009 0.005 0.005 0.006 3 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± C 0.0160.013 0.952 0.976 0.012 0.988 0.0060.007 0.974 0.962 0.010 0.974 0.0050.005 0.986 0.006 0.960 0.008 0.975 0.954 0.0270.031 0.992 0.027 0.966 0.029 0.981 0.961 0.0050.006 0.972 0.957 0.007 0.961 0.0060.007 0.981 0.964 0.008 0.956 0.0190.017 0.995 0.020 0.941 0.028 0.973 0.977 0.0110.012 0.989 0.014 0.947 0.015 0.960 0.987 0.011 0.956 0.007 0.979 0.006 0.968 0.007 0.972 3 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± B Equation 4.4 0.0110.010 -0.082 -0.092 0.008 -0.057 0.0050.006 -0.139 -0.180 0.007 -0.100 0.0050.004 -0.133 0.005 -0.135 0.007 -0.120 -0.087 0.0110.014 -0.127 0.011 -0.148 0.014 -0.105 -0.085 0.0040.005 -0.114 -0.127 0.005 -0.089 0.0050.006 -0.123 -0.141 0.006 -0.082 0.0130.013 -0.085 0.013 -0.145 0.017 -0.092 -0.094 0.0080.010 -0.127 0.011 -0.134 0.010 -0.125 -0.074 0.009 -0.104 0.006 -0.114 0.005 -0.110 0.006 -0.119 3 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± A 0.007 0.083 0.020 0.005 -0.322 -0.345 -0.194 -0.247 -0.245 -0.096 -0.313 -0.316 -0.030 -0.176 -0.330 -0.339 -0.053 -0.208 -0.256 -0.251 -0.136 -0.279 -0.358 -0.157 -0.342 -0.308 -0.046 -0.205 -0.318 -0.331 -0.033 -0.217 0.006 0.004 0.003 0.003 0.003 0.002 0.003 0.003 0.002 0.003 0.002 0.003 0.014 0.013 0.019 0.013 0.003 0.002 0.003 0.003 0.003 0.003 0.003 0.003 0.009 0.007 0.007 0.011 0.006 0.007 0.006 0.006 2 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± C 2009Feb16 2011Jan08 2011Jan09 2011Jan10 2011Jan11 2011Feb16 2011Feb17 2009 Feb 13 0.0030.002 0.977 0.002 0.987 0.002 0.992 0.978 0.0020.001 0.975 0.002 1.000 0.002 0.984 0.995 0.0010.002 0.967 0.001 1.006 0.002 0.984 0.999 0.0050.005 0.970 0.007 1.004 0.005 0.981 1.001 0.0010.001 0.971 0.001 0.996 0.001 0.988 0.988 0.0020.002 0.970 0.002 1.006 0.002 0.983 0.993 0.0050.004 0.988 0.004 0.994 0.005 0.986 0.982 0.0030.004 0.962 0.003 0.989 0.003 0.969 0.998 Equation 4.3 2 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± A -0.227 -0.274 -0.238 -0.221 -0.247 -0.297 -0.257 -0.253 -0.218 -0.269 -0.219 -0.228 -0.235 -0.286 -0.238 -0.248 -0.225 -0.277 -0.235 -0.229 -0.232 -0.285 -0.235 -0.233 -0.241 -0.291 -0.245 -0.235 -0.217 -0.293 -0.230 -0.233 0.004 0.004 0.003 0.003 0.002 0.003 0.002 0.003 0.002 0.002 0.002 0.002 0.011 0.011 0.022 0.011 0.002 0.002 0.002 0.002 0.003 0.004 0.003 0.004 0.006 0.005 0.005 0.006 0.005 0.005 0.004 0.005 1 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± B 0.0020.002 -0.048 0.002 -0.026 0.001 -0.054 -0.054 0.0010.002 -0.044 0.001 -0.025 0.002 -0.063 -0.063 0.0010.001 -0.045 0.001 -0.025 0.001 -0.061 -0.065 0.0040.004 -0.047 0.008 -0.027 0.005 -0.060 -0.064 0.0010.001 -0.048 0.001 -0.031 0.001 -0.055 -0.058 0.0020.002 -0.037 0.002 -0.019 0.002 -0.052 -0.049 0.0030.003 -0.051 0.003 -0.026 0.003 -0.065 -0.037 0.0030.003 -0.061 0.003 -0.029 0.003 -0.059 -0.050 Equation 4.2 1 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± A Table A.9: Standard transformation coefficients for the second calibration -24.915 -24.716 -24.857 -24.802 -24.834 -24.634 -24.770 -24.717 -24.815 -24.601 -24.699 -24.693 -24.741 -24.523 -24.625 -24.618 -24.764 -24.550 -24.650 -24.646 -24.720 -24.501 -24.600 -24.600 -24.748 -24.528 -24.623 -24.638 -24.769 -24.554 -24.662 -24.665 2 3 2 3 2 3 4 2 3 4 2 3 2 3 2 3 4 2 3 4 4 4 4 4 1 1 1 1 1 1 1 1 chip 185 0.012 0.010 0.008 0.008 0.008 0.003 0.006 0.006 0.005 0.004 0.005 0.007 0.019 0.017 0.017 0.018 0.005 0.005 0.005 0.005 0.005 0.006 0.004 0.006 0.012 0.012 0.013 0.015 0.008 0.010 0.009 0.011 4 ˜ ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± C 0.0160.015 0.849 0.012 0.864 0.011 0.887 0.830 0.0100.004 0.859 0.008 0.858 0.010 0.883 0.841 0.0040.003 0.249 0.004 0.295 0.005 0.220 0.314 0.0270.028 0.919 0.027 0.922 0.027 0.930 0.872 0.0060.007 0.889 0.007 0.857 0.007 0.888 0.829 0.0060.008 0.883 0.006 0.867 0.008 0.899 0.833 0.0160.018 0.910 0.017 0.827 0.021 0.899 0.842 0.0100.015 0.906 0.013 0.788 0.014 0.905 0.850 4 ˜ ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± B 0.0040.004 0.241 0.003 0.294 0.003 0.224 0.317 0.0030.002 0.270 0.002 0.332 0.002 0.241 0.320 0.0020.002 0.880 0.002 0.865 0.002 0.899 0.838 0.0050.005 0.214 0.005 0.232 0.005 0.205 0.290 0.0020.002 0.226 0.002 0.294 0.002 0.231 0.308 0.0020.002 0.239 0.002 0.291 0.002 0.227 0.310 0.0050.005 0.189 0.005 0.336 0.006 0.217 0.303 0.0030.005 0.212 0.004 0.395 0.004 0.236 0.279 4 ˜ ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± A 0.203 0.254 0.314 0.371 0.140 0.196 0.266 0.327 0.196 0.259 0.316 0.378 0.174 0.238 0.290 0.356 0.182 0.234 0.293 0.359 0.172 0.232 0.290 0.357 0.201 0.262 0.312 0.376 0.223 0.298 0.343 0.421 0.004 0.004 0.003 0.003 0.005 0.005 0.005 0.005 0.006 0.006 0.005 0.005 0.018 0.020 0.018 0.020 0.005 0.006 0.005 0.005 0.010 0.007 0.007 0.007 0.014 0.010 0.012 0.011 0.011 0.007 0.008 0.008 5 ˜ ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± C 0.0010.001 0.962 0.001 0.910 0.001 0.998 0.970 0.0010.001 0.976 0.001 0.931 0.001 1.023 0.961 0.0010.001 0.989 0.001 0.946 0.001 1.043 0.963 0.0020.003 0.978 0.002 0.955 0.003 1.038 0.969 0.0010.001 0.966 0.001 0.938 0.001 1.027 0.957 0.0020.001 0.946 0.001 0.941 0.001 1.035 0.963 0.0020.001 0.922 0.002 0.918 0.002 1.024 0.955 0.0020.001 0.959 0.001 0.924 0.001 1.030 0.976 Equation 4.8 Equation 4.7 5 ˜ ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± A 2.324 2.308 2.331 2.322 2.311 2.283 2.322 2.304 2.318 2.300 2.304 2.302 2.316 2.306 2.314 2.302 2.322 2.313 2.320 2.306 2.329 2.315 2.322 2.305 2.302 2.289 2.302 2.279 2.301 2.292 2.311 2.289 2009Feb16 2011Jan08 2011Jan09 2011Jan10 2011Jan11 2011Feb16 2011Feb17 2009 Feb 13 0.005 0.005 0.004 0.003 0.005 0.003 0.003 0.003 0.003 0.002 0.003 0.002 0.006 0.005 0.006 0.006 0.003 0.002 0.003 0.003 0.003 0.003 0.003 0.003 0.007 0.005 0.006 0.006 0.006 0.006 0.005 0.005 4 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± D 0.0120.011 0.033 0.008 0.028 0.008 0.023 0.023 0.0090.004 0.009 0.007 0.033 0.007 0.014 0.023 0.0050.003 0.011 0.005 0.031 0.004 0.017 0.029 0.0190.016 0.015 0.017 0.036 0.017 0.025 0.029 0.0050.005 0.021 0.005 0.036 0.005 0.028 0.024 0.0060.006 0.013 0.005 0.033 0.006 0.020 0.026 0.0130.013 0.013 0.014 0.039 0.017 0.023 0.033 0.0090.012 0.019 0.009 0.033 0.012 0.030 0.023 4 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± C 0.0160.014 0.878 0.012 0.886 0.011 0.891 0.834 0.0100.004 0.868 0.008 0.891 0.009 0.894 0.857 0.0060.004 0.891 0.005 0.894 0.006 0.914 0.857 0.0270.026 0.912 0.026 0.905 0.025 0.926 0.871 0.0060.006 0.903 0.006 0.892 0.007 0.905 0.843 0.0060.007 0.894 0.006 0.914 0.007 0.917 0.859 0.0160.017 0.919 0.017 0.879 0.021 0.919 0.893 0.0100.016 0.915 0.012 0.832 0.014 0.934 0.878 Equation 4.5 4 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± B Table A.10: Standard transformation coefficients for the second calibration (Cont.) 0.0060.005 0.229 0.005 0.283 0.004 0.235 0.326 0.0050.003 0.263 0.004 0.308 0.004 0.235 0.316 0.0030.003 0.234 0.003 0.273 0.003 0.212 0.311 0.0050.006 0.221 0.005 0.267 0.005 0.205 0.287 0.0030.002 0.219 0.003 0.270 0.003 0.227 0.306 0.0030.003 0.231 0.003 0.250 0.003 0.214 0.295 0.0080.007 0.187 0.007 0.293 0.009 0.204 0.271 0.0050.006 0.210 0.006 0.356 0.006 0.212 0.261 4 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± A 0.173 0.230 0.294 0.352 0.133 0.168 0.254 0.305 0.187 0.233 0.301 0.351 0.168 0.216 0.280 0.344 0.165 0.203 0.269 0.338 0.162 0.204 0.273 0.333 0.190 0.226 0.291 0.341 0.209 0.270 0.319 0.399 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 1 1 1 1 1 1 1 1 chip 186 APPENDIX A. TABLES

Table A.11: Typical physical parameters for diﬀerent type stars and expected photometric indexes for main sequence stars (log g =4.2) according to Castelli & Kurucz (2004). This information is used in Sect.6.5 to study the eﬀect of binarity. SP Teff (K) MV Mass(M) [c1] [m1] Hβ (b − y)0 B0 29200 -3.3 16.00 -0.066 0.035 2.593 -0.117 B2 21000 -1.9 10.50 0.131 0.064 2.645 -0.094 B5 15200 -0.4 5.40 0.397 0.092 2.713 -0.062 B8 12300 0.7 3.50 0.682 0.113 2.787 -0.040 A0 9600 1.5 2.60 1.019 0.171 2.916 0.004 A2 9040 1.8 2.20 1.028 0.195 2.929 0.026 A5 8310 2.2 1.90 0.946 0.221 2.899 0.083 F0 7350 3.0 1.60 0.675 0.232 2.775 0.192 F2 7050 3.3 1.50 0.579 0.241 2.732 0.228 F5 6700 3.7 1.35 0.472 0.260 2.687 0.270 G0 6050 4.7 1.08 0.293 0.342 2.616 0.360 G2 5800 5.0 1.00 0.2415 0.393 2.596 0.399 G5 5660 5.2 0.95 0.218 0.425 2.587 0.421 G8 5440 5.6 0.85 0.184 0.486 2.574 0.459 K0 5240 6.0 0.83 0.160 0.551 2.562 0.495 K2 4960 6.4 0.78 0.146 0.645 2.549 0.546 K5 4400 7.4 0.68 0.206 0.800 2.512 0.676 Appendix B

MV calibration for each spectral type

The absolute magnitude for a main sequence star can be associated to a spectral type following, e.g. Wegner (2007). These authors compute the mean absolute magnitude for diﬀerent sets of Hipparcos stars with known spectral types. The authors do not take into account the Malmquist bias, so we have corrected it following Luri et al. (1993). A disk scaleheight hz=200pc is imposed (the results do not change substantially for 100pc or 300pc) and an intrinsic dispersion of the population σM =0.6 (A0 stars from Luri (1995)). Since we are dealing with the Hipparcos catalog, Vlim = 8 is used. In Fig.B.1 we see the MV for diﬀerent main sequence spectral types provided by Wegner (2007), as well as the values once corrected for the Malmquist bias. The corrected values are used in Table 9.2 in order to associate the MVlim with an spectral type.

187 188 APPENDIX B. MV CALIBRATION FOR EACH SPECTRAL TYPE

V M

6 O5 O6 O7 O8 O9 O9.5 B0 B0.5 B1 B1.5 B2 B2.5 B3 B4 B5 B6 B7 B8 B9 B9.5 A0 A1 A2 A3 A4 A5 A6 A7 A8 A9 SP

Figure B.1: MV magnitude for diﬀerent main sequence spectral types. Dashed blue line gives the values provided by Wegner (2007), and continuous green line shows the Malmquist corrected values. Appendix C

Surface density distribution plots

Next figures and Tables provide all the available distance distribution plots for the different samples and options discussed in Chapters 9 and 10. Table C.1 provides the values for the scale length hR and the surface density at the solar position Σ obtained for the different fits. Model Bforthehz values have been selected in all cases, i.e. hz=100pc for B5 stars and hz=200pc for A5 stars. Figures from C.1 to C.8 show the surface density distributions for each case, with the fitted exponential, and the limits used for the fits. In each figure we find the results for the six samples MB-S1, MB-S2, CS-MB, EC-S1, EC-S2 and CS-EC. And the different figures show the results for inner and outer sky areas, knuth and 200pc bin size, and using the more and less restrictive options for the AV maximum at 3 kpc. Then, Table C.2 shows the results where the points close to the spiral arm (i.e., between 1400 and 2000pc) have been excluded from the fit. Again, fits for different samples, bin sizes, sky areas and AVmax(3 kpc) are provided in the table, as well as in the figures C.1 to C.8. There we show also which of the points have been used for the fit.

189 190 APPENDIX C. SURFACE DENSITY DISTRIBUTION PLOTS

Table C.1: Scale length hz and surface density at the Sun position σ obtained from the diﬀerent ﬁts. All the samples (S1, S2 and CS), physical parameters methods (EC and MB), sky areas (inner and outer), bin sizes (knuth and 200pc), and maximum absorptions at 3 kpc (AV (r)+

σAV (r)andAV (r)) have been taken into account. S1 S2 CS area hR Σ hR Σ hR Σ

bin=knuth, AVmax(r)=AV (r)+σAV (r) MB in 2000±500 0.026±0.006 1800±400 0.025±0.006 2000±500 0.010±0.002 EC in 1000±100 0.039±0.006 900±100 0.041±0.005 1300±600 0.009±0.005 MB all 2400± 300 0.005±0.001 2100±400 0.005±0.001 2400±1300 0.001±0.000 EC all 3100±2600 0.001±0.001 2200±1100 0.002±0.001 3400±4500 0.000±0.000 bin=knuth, AVmax(r)=AV (r) MB in 1400±100 0.104±0.011 1300±100 0.100±0.012 1500±200 0.049±0.006 EC in 1200± 200 0.119±0.023 1100±100 0.122±0.025 1100±100 0.086±0.014 MB all 1500+-200 0.035+-0.005 1400+-100 0.032+-0.004 1700+-300 0.010+-0.002 EC all 1000+-100 0.032+-0.004 1100+-100 0.022+-0.003 1900+-600 0.004+-0.001

bin=200pc, AVmax(r)=AV (r)+σAV (r) MB in 1700±300 0.032±0.005 1600±200 0.031±0.006 1700±300 0.013±0.002 EC in 1100±100 0.035±0.006 1000±100 0.035±0.008 1400±400 0.009±0.003 MB all 2100±400 0.006±0.001 1900±400 0.005±0.001 2700±1600 0.001±0.000 EC all 2900±1400 0.002±0.001 2900±1700 0.001±0.000 4200±6100 0.000±0.000 bin=200pc, AVmax(r)=AV (r) MB in 1500±200 0.094±0.014 1400±200 0.091±0.013 1500±200 0.049±0.006 EC in 1100±100 0.124±0.018 1100±100 0.128±0.018 1100±100 0.083±0.011 MB all 1600±200 0.031±0.004 1400±200 0.029±0.005 1700±300 0.010±0.002 EC all 1200± 100 0.024±0.004 1100±100 0.022±0.003 2100±700 0.004±0.001 191

0.007 0.016 0.014 hR =2000 ± 500 h =1800 ± 400 R 0.006 h =2000 ± 500 0.014 Σ =0.026 ±0.006 R 0.012 Σ =0.025 ±0.006 Σ =0.010 ±0.002 0.012 0.005 0.010

) 0.010 2 0.004 0.008 /pc 0.008 ⋆ 0.003 0.006 Σ( 0.006 0.004 0.002 0.004 0.001 0.002 0.002 MBS1in MBS2in CSMBin 0.000 0.000 0.000 0.016 hR =1000 ± 100 h = 900 ± 100 0.012 R hR =1300 ± 600 0.014 Σ =0.039 ±0.006 Σ =0.041 ±0.005 0.004 Σ =0.009 ±0.005 0.012 0.010

) 0.010 0.003 2 0.008

/pc 0.008 ⋆ 0.006 0.002 Σ( 0.006 0.004 0.004 0.001 0.002 0.002 CSECin ECS1in ECS21in 0.000 0.000 0.000 500 1000 1500 2000 2500 3000 3500 4000 500 1000 1500 2000 2500 3000 3500 4000 500 1000 1500 2000 2500 3000 3500 4000 distance (pc) distance (pc) distance (pc)

Figure C.1: Surface density distribution in the anticenter direction for the six samples. Inner sky area for all of them is used. Knuth bin size and restrictive value of the maximum absorption at 3 kpc are used. Continuous line and wider blue dots indicate the range used for the fit. Smaller blue dots and dashed line indicate points not used for the fit. Pink line shows the fitted exponential, with the values for the zero point (in stars per pc2) and the radial scale length (in parsecs) indicated. Vertical red lines show the completeness limits at 1.2 and 3 kpc. 192 APPENDIX C. SURFACE DENSITY DISTRIBUTION PLOTS

0.0035 0.0010 0.0030 h =2400 ± 300 R hR =2100 ± 400 h =2400 ±1300 0.0030 Σ =0.0047 ±0.0009 R Σ =0.0050 ±0.0005 0.0025 0.0008 Σ =0.0012 ±0.0005 0.0025 0.0020 ) 0.0006 2 0.0020 CSMBall /pc 0.0015 ⋆ 0.0015 0.0004 Σ( 0.0010 0.0010 0.0002 0.0005 0.0005 MBS1all MBS2all 0.0000 0.0000 0.0000 0.0014 h =3400 ±4500 h =3100 ±2600 h =2200 ±1100 0.00035 R R 0.0012 R Σ =0.0003 ±0.0002 0.0012 Σ =0.0015 ±0.0008 Σ =0.0015 ±0.0006 0.00030 0.0010 0.0010 0.00025 )

2 0.0008 0.0008 0.00020 /pc

⋆ 0.0006 0.0006 0.00015 Σ( 0.0004 0.0004 0.00010

0.0002 0.0002 0.00005 ECS1all ECS2all CSECall 0.0000 0.0000 0.00000 distance (pc) distance (pc) distance (pc)

Figure C.2: Same as Fig.C.1 for all the sky area, knuth bin size, and restrictive maximum absorption at 3 kpc.

0.040 0.020 0.035 hR =1300 ± 100 h =1500 ± 200 0.04 hR =1400 ± 100 R Σ =0.104 ±0.011 Σ =0.100 ±0.012 Σ =0.049 ±0.006 0.030 0.015 0.03

) 0.025 2

/pc 0.020

⋆ 0.010 0.02

Σ( 0.015

0.010 0.01 0.005 0.005 MBS1in MBS2in CSMBin 0.00 0.000 0.000 h =1200 ± 200 R 0.040 h =1100 ± 100 R 0.025 hR =1100 ± 100 0.04 Σ =0.119 ±0.023 Σ =0.122 ±0.025 0.035 Σ =0.086 ±0.014 0.030 0.020

) 0.03 2 0.025 0.015 /pc

⋆ 0.020 0.02 Σ( 0.015 0.010

0.01 0.010 0.005 0.005 ECS1in ECS21in CSECin 0.00 0.000 0.000 500 1000 1500 2000 2500 3000 3500 4000 500 1000 1500 2000 2500 3000 3500 4000 500 1000 1500 2000 2500 3000 3500 4000 distance (pc) distance (pc) distance (pc)

Figure C.3: Same as Fig.C.1 for inner sky area, knuth bin size, and less restrictive maximum absorption at 3 kpc. 193

0.014 0.014 h =1500 ± 200 0.005 R 0.012 hR =1400 ± 100 hR =1700 ± 300 Σ =0.0346 ±0.0048 Σ =0.0099 ±0.0018 0.012 Σ =0.0317 ±0.0036 0.010 0.004 0.010 )

2 0.008 0.008 0.003 /pc

⋆ 0.006 0.006 Σ( 0.002

0.004 0.004 0.001 0.002 0.002 MBS1all MBS2all CSMBall 0.000 0.000 0.000 0.012 0.0030 0.008 hR =1900 ± 600 hR =1000 ± 100 hR =1100 ± 100 Σ =0.0045 ±0.0014 0.010 Σ =0.0319 ±0.0036 0.007 Σ =0.0224 ±0.0035 0.0025

0.006

) 0.008 0.0020

2 0.005

/pc 0.006 0.0015 ⋆ 0.004 Σ( 0.004 0.003 0.0010 0.002 0.002 0.0005 0.001 ECS1all ECS2all CSECall 0.000 0.000 0.0000 distance (pc) distance (pc) distance (pc)

Figure C.4: Same as Fig.C.1 for all the sky area, knuth bin size, and less restrictive maximum absorption at 3 kpc.

0.007 0.016 0.014 hR =1700 ± 300 h =1600 ± 200 R 0.006 h =1700 ± 300 0.014 Σ =0.032 ±0.005 R 0.012 Σ =0.031 ±0.006 Σ =0.013 ±0.002 0.012 0.005 0.010

) 0.010 2 0.004 0.008 /pc 0.008 ⋆ 0.003 0.006 Σ( 0.006 0.004 0.002 0.004 0.001 0.002 0.002 MBS1in MBS2in CSMBin 0.000 0.000 0.000 0.016 hR =1100 ± 100 h =1000 ± 100 0.012 R hR =1400 ± 400 0.014 Σ =0.035 ±0.006 Σ =0.035 ±0.008 0.004 Σ =0.009 ±0.003 0.012 0.010

) 0.010 0.003 2 0.008

Figure C.5: Same as Fig.C.1 for the inner sky area, 200pc bin size, and restrictive maximum absorption at 3 kpc. 194 APPENDIX C. SURFACE DENSITY DISTRIBUTION PLOTS

0.0040

0.0035 0.0030 h =1900 ± 400 R 0.0010 hR =2700 ±1600 hR =2100 ± 400 Σ =0.0053 ±0.0012 Σ =0.0011 ±0.0005 0.0030 0.0025 Σ =0.0056 ±0.0010 0.0008

) 0.0025 0.0020 2

/pc 0.0020 0.0006

⋆ 0.0015

Σ( 0.0015 0.0004 0.0010 0.0010

0.0005 0.0002 0.0005 CSMBall MBS1all MBS2all 0.0000 0.0000 0.0000 0.0014 h =4200 ±6100 h =2900 ±1400 h =2900 ±1700 0.00035 R R 0.0012 R Σ =0.0003 ±0.0002 0.0012 Σ =0.0016 ±0.0005 Σ =0.0012 ±0.0005 0.00030 0.0010 0.0010 0.00025 )

2 0.0008 0.0008 0.00020 /pc

⋆ 0.0006 0.0006 0.00015 Σ( 0.0004 0.0004 0.00010

0.0002 0.0002 0.00005 ECS1all ECS2all CSECall 0.0000 0.0000 0.00000 distance (pc) distance (pc) distance (pc)

Figure C.6: Same as Fig.C.1 for all the sky area, 200pc bin size, and restrictive maximum absorption at 3 kpc.

0.040 0.020 0.035 hR =1400 ± 200 h =1500 ± 200 0.04 hR =1500 ± 200 R Σ =0.094 ±0.014 Σ =0.091 ±0.013 Σ =0.049 ±0.006 0.030 0.015 0.03

) 0.025 2

/pc 0.020

⋆ 0.010 0.02

Σ( 0.015

0.010 0.01 0.005 0.005 MBS1in MBS2in CSMBin 0.00 0.000 0.000 h =1100 ± 100 R 0.040 h =1100 ± 100 R 0.025 hR =1100 ± 100 0.04 Σ =0.124 ±0.018 Σ =0.128 ±0.018 0.035 Σ =0.083 ±0.011 0.030 0.020

) 0.03 2 0.025 0.015 /pc

⋆ 0.020 0.02 Σ( 0.015 0.010

Figure C.7: Same as Fig.C.1 for the inner sky area, 200pc bin size, and less restrictive maximum absorption at 3 kpc. 195

Table C.2: Values for the scale length hz and surface density (in pc) at the Sun position σ (in stars/pc2) obtained from the diﬀerent ﬁts where the points between 1400 pc and 2000 pc. All the samples (S1, S2 and CS), physical parameters methods (EC and MB), sky areas (inner and outer), bin sizes (knuth and 200pc), and maximum absorptions at 3 kpc (AV (r)+σAV (r)and AV (r)) have been taken into account. S1 S2 CS area hR Σ hR Σ hR Σ

bin=knuth, AVmax(r)=AV (r)+σAV (r) MB in 2600±400 0.019±0.002 2200±300 0.019±0.002 2200±600 0.008±0.002 EC in 1000±100 0.040±0.008 1000±100 0.040±0.007 1600±700 0.006±0.004 MB all 2700± 300 0.004±0.000 2300±200 0.004±0.000 3000±2100 0.001±0.000 EC all 1800±1200 0.002±0.002 2000± 600 0.002±0.000 800±400 0.003±0.004 bin=knuth, AVmax(r)=AV (r) MB in 1400±100 0.105±0.012 1300±100 0.103±0.011 1600±100 0.044±0.005 EC in 1200±200 0.116±0.028 1100±200 0.119±0.027 1000±100 0.099±0.013 MB all 1600±100 0.029±0.003 1400±100 0.030±0.004 1900±200 0.008±0.001 EC all 1000±100 0.032±0.004 1100±100 0.021±0.003 2100±300 0.004±0.001

bin=200pc, AVmax(r)=AV (r)+σAV (r) MB in 2000±300 0.025±0.004 1800±200 0.025±0.004 1800±200 0.011±0.001 EC in 1100±100 0.032±0.005 1100±100 0.030±0.007 1600±500 0.006±0.003 MB all 2700±400 0.004±0.001 2300±200 0.004±0.000 5200±4600 0.001±0.000 EC all 2600±900 0.002±0.000 2700±1400 0.001±0.001 7100±6100 0.000±0.000 bin=200pc, AVmax(r)=AV (r) MB in 1600±200 0.083±0.010 1500±100 0.081±0.009 1600±100 0.044±0.005 EC in 1100±100 0.127±0.021 1000±100 0.129±0.020 1100±100 0.083±0.015 MB all 1700±100 0.028±0.002 1500±100 0.026±0.003 1900±200 0.008±0.001 EC all 1300±100 0.021±0.003 1200±100 0.019±0.003 2700±600 0.003±0.001 196 APPENDIX C. SURFACE DENSITY DISTRIBUTION PLOTS

0.014 0.014 h =1600 ± 200 0.005 R 0.012 hR =1400 ± 200 hR =1700 ± 300 Σ =0.0313 ±0.0041 Σ =0.0099 ±0.0018 0.012 Σ =0.0288 ±0.0048 0.010 0.004 0.010 )

2 0.008 0.008 0.003 /pc

⋆ 0.006 0.006 Σ( 0.002

0.004 0.004 0.001 0.002 0.002 MBS1all MBS2all CSMBall 0.000 0.000 0.000 0.012 0.0030 0.008 hR =2100 ± 700 hR =1200 ± 100 hR =1100 ± 100 Σ =0.0040 ±0.0012 0.010 Σ =0.0244 ±0.0041 0.007 Σ =0.0218 ±0.0034 0.0025

0.006

) 0.008 0.0020

2 0.005

/pc 0.006 0.0015 ⋆ 0.004 Σ( 0.004 0.003 0.0010 0.002 0.002 0.0005 0.001 ECS1all ECS2all CSECall 0.000 0.000 0.0000 distance (pc) distance (pc) distance (pc)

Figure C.8: Same as Fig.C.1 for all the sky area, 200pc bin size, and less restrictive maximum absorption at 3 kpc. 197

0.007 0.016 0.014 hz =2600 ± 400 h =2200 ± 300 z 0.006 h =2200 ± 600 0.014 Σ =0.019 ±0.002 z 0.012 Σ =0.019 ±0.002 Σ =0.008 ±0.002 0.012 0.005 0.010

) 0.010 2 0.004 0.008 /pc 0.008 ⋆ 0.003 0.006 Σ( 0.006 0.004 0.002 0.004 0.001 0.002 0.002 MBS1in MBS2in CSMBin 0.000 0.000 0.000 0.016 hz =1000 ± 100 h =1000 ± 100 0.012 z hz =1600 ± 700 0.014 Σ =0.040 ±0.008 Σ =0.040 ±0.007 0.004 Σ =0.006 ±0.004 0.012 0.010

) 0.010 0.003 2 0.008

Figure C.9: Surface density distribution in the anticenter direction for the six samples. Inner sky area for all of them is used. Knuth bin size and restrictive value of the maximum absorption at 3 kpc are used. Green dots indicate the points used for the fit. Smaller blue dots and dashed line indicate points not used for the fit. Pink line shows the fitted exponential, with the values for the zero point (in stars per pc2) and the scale length (in parsecs) indicated. Vertical red lines show the limits at 1.2 and 3 kpc. 198 APPENDIX C. SURFACE DENSITY DISTRIBUTION PLOTS

0.0035 0.0010 0.0030 h =2700 ± 300 z hz =2300 ± 200 h =3000 ±2100 0.0030 Σ =0.0040 ±0.0002 z Σ =0.0043 ±0.0004 0.0025 0.0008 Σ =0.0009 ±0.0004 0.0025 0.0020 ) 0.0006 2 0.0020 CSMBall /pc 0.0015 ⋆ 0.0015 0.0004 Σ( 0.0010 0.0010 0.0002 0.0005 0.0005 MBS1all MBS2all 0.0000 0.0000 0.0000 0.0014 h = 800 ± 400 h =1800 ±1200 h =2000 ± 600 0.00035 z z 0.0012 z Σ =0.0029 ±0.0036 0.0012 Σ =0.0025 ±0.0024 Σ =0.0016 ±0.0005 0.00030 0.0010 0.0010 0.00025 )

2 0.0008 0.0008 0.00020 /pc

⋆ 0.0006 0.0006 0.00015 Σ( 0.0004 0.0004 0.00010

0.0002 0.0002 0.00005 ECS1all ECS2all CSECall 0.0000 0.0000 0.00000 distance (pc) distance (pc) distance (pc)

Figure C.10: Same as Fig.C.9 for all the sky area, knuth bin size, and restrictive maximum absorption at 3 kpc.

0.040 0.020 0.035 hz =1300 ± 100 h =1600 ± 100 0.04 hz =1400 ± 100 z Σ =0.105 ±0.012 Σ =0.103 ±0.011 Σ =0.044 ±0.005 0.030 0.015 0.03

) 0.025 2

/pc 0.020

⋆ 0.010 0.02

Σ( 0.015

0.010 0.01 0.005 0.005 MBS1in MBS2in CSMBin 0.00 0.000 0.000 h =1200 ± 200 z 0.040 h =1100 ± 200 z 0.025 hz =1000 ± 100 0.04 Σ =0.116 ±0.028 Σ =0.119 ±0.027 0.035 Σ =0.099 ±0.013 0.030 0.020

) 0.03 2 0.025 0.015 /pc

⋆ 0.020 0.02 Σ( 0.015 0.010

Figure C.11: Same as Fig.C.9 for the inner sky area, knuth bin size, and less restrictive maximum absorption at 3 kpc. 199

0.014 0.014 h =1600 ± 100 0.005 z 0.012 hz =1400 ± 100 hz =1900 ± 200 Σ =0.0289 ±0.0029 Σ =0.0082 ±0.0009 0.012 Σ =0.0304 ±0.0038 0.010 0.004 0.010 )

2 0.008 0.008 0.003 /pc

⋆ 0.006 0.006 Σ( 0.002

0.004 0.004 0.001 0.002 0.002 MBS1all MBS2all CSMBall 0.000 0.000 0.000 0.012 0.0030 0.008 hz =2100 ± 300 hz =1000 ± 100 hz =1100 ± 100 Σ =0.0037 ±0.0006 0.010 Σ =0.0321 ±0.0035 0.007 Σ =0.0206 ±0.0034 0.0025

0.006

) 0.008 0.0020

2 0.005

/pc 0.006 0.0015 ⋆ 0.004 Σ( 0.004 0.003 0.0010 0.002 0.002 0.0005 0.001 ECS1all ECS2all CSECall 0.000 0.000 0.0000 distance (pc) distance (pc) distance (pc)

Figure C.12: Same as Fig.C.9 for all the sky area, knuth bin size, and less restrictive maximum absorption at 3 kpc.

0.007 0.016 0.014 hz =2000 ± 300 h =1800 ± 200 z 0.006 h =1800 ± 200 0.014 Σ =0.025 ±0.004 z 0.012 Σ =0.025 ±0.004 Σ =0.011 ±0.001 0.012 0.005 0.010

) 0.010 2 0.004 0.008 /pc 0.008 ⋆ 0.003 0.006 Σ( 0.006 0.004 0.002 0.004 0.001 0.002 0.002 MBS1in MBS2in CSMBin 0.000 0.000 0.000 0.016 hz =1100 ± 100 h =1100 ± 100 0.012 z hz =1600 ± 500 0.014 Σ =0.032 ±0.005 Σ =0.030 ±0.007 0.004 Σ =0.006 ±0.003 0.012 0.010

) 0.010 0.003 2 0.008

Figure C.13: Same as Fig.C.9 for the inner sky area, 200pc bin size, and restrictive maximum absorption at 3 kpc. 200 APPENDIX C. SURFACE DENSITY DISTRIBUTION PLOTS

0.0040

0.0035 0.0030 h =2300 ± 200 z 0.0010 hz =5200 ±4600 hz =2700 ± 400 Σ =0.0039 ±0.0004 Σ =0.0007 ±0.0003 0.0030 0.0025 Σ =0.0041 ±0.0005 0.0008

) 0.0025 0.0020 2

/pc 0.0020 0.0006

⋆ 0.0015

Σ( 0.0015 0.0004 0.0010 0.0010

0.0005 0.0002 0.0005 CSMBall MBS1all MBS2all 0.0000 0.0000 0.0000 0.0014 h =7100 ±26100 h =2600 ± 900 h =2700 ±1400 0.00035 z z 0.0012 z Σ =0.0002 ±0.0002 0.0012 Σ =0.0016 ±0.0005 Σ =0.0012 ±0.0005 0.00030 0.0010 0.0010 0.00025 )

2 0.0008 0.0008 0.00020 /pc

⋆ 0.0006 0.0006 0.00015 Σ( 0.0004 0.0004 0.00010

0.0002 0.0002 0.00005 ECS1all ECS2all CSECall 0.0000 0.0000 0.00000 distance (pc) distance (pc) distance (pc)

Figure C.14: Same as Fig.C.9 for all the sky area, 200pc bin size, and restrictive maximum absorption at 3 kpc.

0.040 0.020 0.035 hz =1500 ± 100 h =1600 ± 100 0.04 hz =1600 ± 200 z Σ =0.083 ±0.010 Σ =0.081 ±0.009 Σ =0.044 ±0.005 0.030 0.015 0.03

) 0.025 2

/pc 0.020

⋆ 0.010 0.02

Σ( 0.015

0.010 0.01 0.005 0.005 MBS1in MBS2in CSMBin 0.00 0.000 0.000 h =1100 ± 100 z 0.040 h =1000 ± 100 z 0.025 hz =1100 ± 100 0.04 Σ =0.127 ±0.021 Σ =0.129 ±0.020 0.035 Σ =0.083 ±0.015 0.030 0.020

) 0.03 2 0.025 0.015 /pc

⋆ 0.020 0.02 Σ( 0.015 0.010

Figure C.15: Same as Fig.C.9 for the inner sky area, 200pc bin size, and less restrictive maximum absorption at 3 kpc. 201

0.014 0.014 h =1700 ± 100 0.005 z 0.012 hz =1500 ± 100 hz =1900 ± 200 Σ =0.0276 ±0.0023 Σ =0.0082 ±0.0009 0.012 Σ =0.0257 ±0.0028 0.010 0.004 0.010 )

2 0.008 0.008 0.003 /pc

⋆ 0.006 0.006 Σ( 0.002

0.004 0.004 0.001 0.002 0.002 MBS1all MBS2all CSMBall 0.000 0.000 0.000 0.012 0.0030 0.008 hz =2700 ± 600 hz =1300 ± 100 hz =1200 ± 100 Σ =0.0028 ±0.0005 0.010 Σ =0.0214 ±0.0029 0.007 Σ =0.0192 ±0.0030 0.0025

0.006

) 0.008 0.0020

2 0.005

/pc 0.006 0.0015 ⋆ 0.004 Σ( 0.004 0.003 0.0010 0.002 0.002 0.0005 0.001 ECS1all ECS2all CSECall 0.000 0.000 0.0000 distance (pc) distance (pc) distance (pc)

Figure C.16: Same as Fig.C.9 for all the sky area, 200pc bin size, and less restrictive maximum absorption at 3 kpc. 202 APPENDIX C. SURFACE DENSITY DISTRIBUTION PLOTS Appendix D

Changing the stars in the gap

As discussed in Sect. 5.1 and Chapter 6, the stars located in the gap of the [m1] − [c1]plotare very difficult to classify, since they could belong to both, early or late type stars. For that reason, in order to study whether the possible missclassification can change our results we do here a test of changing the classification of these stars. We will use the parameter Nside (see Sect.6.7) in order to detect those stars. i.e., all the stars with Nside < 70 will be re-allocated to the other (B) side of the gap, using the parameters computed through the Pmax parameter (see Sect.6.6.3). In comparison with the MB-S1 sample, we will call this new sample with the physical parameters for some stars changed like MB-S1(B). Once we changed the physical parameters for all these stars (3708 of the 35974 where changed, i.e. 11%), we follow the same restrictions in order to re-create the MB-S1(3) original sample, now named MB-S1(B3). That is:

• Remove emission line stars according to IPHAS data (see Sect. 9.1).

• Remove stars colder than Teff =7000K (see Sect. 9.1). • Split between inner and outer sky areas (see Sect.9.1).

• Select the stars in the MV range to have the sample complete up to 3 kpc (see Sect. 9.3 and Table 9.2).

In Fig.D.1 we compare the surface density distribution in the anticenter for the two new samples MB-S1(B3)in and MB-S1(B3)all and compare them with the original samples MB-S1(3)in and MB-S1(3)all. We can see the the distribution are slightly diﬀerent, but the main features remain unchanged. Specially the overdensity due to the Perseus arm is still perfectly visible, even when we change the location of the stars that are doubtfully located at one or the other side of the gap. That means that even some of these stars may be wrongly classiﬁed, the main results of the thesis will not change.

203 204 APPENDIX D. CHANGING THE STARS IN THE GAP

0.020 MB-S1(3)in MB-S1(B3)in ) 2

/pc 0.015 ⋆ (

0.010 surface density 0.005

0.000

0.006 MB-S1(3)all MB-S1(B3)all

) 0.005 2 /pc ⋆

( 0.004

0.003

0.002 surface density

0.001

0.000 500 1000 1500 2000 2500 3000 3500 500 1000 1500 2000 2500 3000 3500 distance(pc) distance(pc)

Figure D.1: Star density distribution in the anticenter direction for the four samples, the two original MB-S1(3)in and MB-S1(3)all (already visible in previous plots) and the new samples with the doubtful stars located at the other side of the gap: MB-S1(B3)in and MB-S1(B3)all. The pink line shows the ﬁt between 1 and 3 kpc. Appendix E

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