利用UKIDSS-UDS資料來統計紅移1到3之間的紫外線光度密度

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(1)UKIDSS-UDS: UV-Luminosity density at 1 < z < 3. Ching-Min Lo. Supervisor: Sébastien Foucaud. January, 2013 National Taiwan Normal University, Taiwan.

(2) –2– ABSTRACT. The star formation history is a key-element to understand galaxy evolution and formation. Recent studies have shown that the star-formation rate peaks at redshift z=1-3 and then decline to its local value. The physical processes responsible for the sudden quenching of star-formation are still unknown. In order to better understand the origin of these e↵ects, we propose in this study to use the UV-luminosity as an indicator of the Star-formation rate. We take advantage of our deep NIR/optical data from the UKIDSS-UDS/SXDS survey and our very deep CFHT U-band data to compute the luminosity function of galaxies at z=1-3. Then we fit a Schechter function and integrate to compute the luminosity density to explore the evolution of the star-formation rate. Subject headings: star-forming galaxy, star-formation rate, star formation history.

(3) Contents 1. Introduction 1.1. Cosmic star formation rate 1.2. Tracers of star formation rate 1.3. Thesis structure. 2. Data 2.1. Photometric redshift 2.2. Absolute magnitude 2.3. Stellar mass. 3. Luminosity Function 4. B-band Luminosity Function up to z ~ 2 5. UV Luminosity Function at z=1-3 6. UV Luminosity Density at z=1-3 7. UV Luminosity Density of Low Stellar Mass System 8. Conclusion and Summary 9. Reference Appendix A1 Appendix A2 Appendix A3. -3-4-4-6-10-14-17-19-21-24-30-. -33-35-37-40-43-. -48-.

(4) –3– 1. 1.1.. Introduction. Cosmic star formation rate. One of the more important studies of galaxy evolution is the evolution of star-formation rate (SFR) over time. Combining high-redshift results with those from local observations, we now have an unprecedented view of galaxies from the epoch of re-ionization to the present days. The SFR of galaxies increases from high redshift to z ⇠ 3, peaks at z = 2. 3,. then drops rapidly to its present value (Bouwens et al. 2007; Reddy et al. 2008; Cucciati et al.2012). The exact quenching processes responsible for the decline of star formation are still unknown. We also identified a phenomenon called downsizing, corresponding to that SFR contribution was dominated by massive galaxies at high redshift but dominated by small galaxies in the present days (Cowie et al. 1996). Because the physical processes responsible for those phenomena are still unknown, several studies have been performed to estimate the di↵erent properties of galaxies and their environment. For example, we can investigate the relation between environmental density and star formation to see the e↵ect of environment; Quadri et al. (2012) compared the SFR in di↵erent stellar mass to explore the evolution of SFR with mass. Merger rate and feedback process are also expected to play important role on evolution of the star formation (Hopkins et al. 2006). The fact that this evolution is di↵erent for di↵erent luminosities opens up new avenues of improving our understanding of how galaxies form and evolve at high redshift. In this work, thanks to our deeper and comprehensive data set, we aim to span a wide redshift range (1< z <3) and measure more accurately the luminosity density (LD) to explore the evolution of SFR. Besides, we measure the LD of di↵erent stellar-mass selected samples to investigate the role played by stellar mass in such evolution. This is the first step to better understand how galaxies evolve, and which physcial processes dominate the cosmic star formation rate..

(5) –4– 1.2.. Tracers of Star Formation Rate. Di↵erent SFR indicators are measured at di↵erent wavelengths with di↵erent methods. These include: LD estimated from the infrared (IR) produced by the re-emission of ultraviolet (UV) photons by dust (e.g., Caputi et al. 2007; P` erez-Gonz`alez et al. 2005; Reddy et al. 2008); nebular emission lines such as H↵, H. and [OII], produced by there. combination of ionized gas surrounding hot young OB stars (e.g., Tresse et al. 2002; Sawicki et al. 2005; Reddy et al. 2008); X-ray emission produced by X-ray binary systems in late-type galaxies (Norman et al. 2004; Lehmer et al. 2008); and SFR from radio emission produced by relativistic electrons in supernova remnants (Condon 1992; Seymour et al. 2008). But more directly, LD have been measured from the UV luminosities of galaxies produced from OB stars (Reddy et al. 2008; Oesch et al. 2010; Cucciati et al. 2012). Except potential contamination by other objects such as stars and AGNs, UV is the best tracer of SFR as purely relying on new stars luminosity. Di↵erent tracers of SFR, namely Ha, IR and UV, have been compared to each others by Hirashita et al. (2003): H↵ is a very reliable indicator, if the Balmer decrement is measured precisely enough to correct for the extinction of H↵ photons; the IR luminosity traces the SFR quite well but there is a risk that the SFR is underestimated for SFR  1 M yr 1 ; UV-luminosites should be corrected for dust extinction. Therefore, extinction is the main problem in UV, therefore, we can use both UV and IR to explore the SFRH (Reddy et al. 2008). It is a better way to trace SFR and we plan to use both indicators in the future.. 1.3.. Thesis structure. In this work, we use UV luminosity function (LF) to a trace SFR as a first step. In the future we will use longer wavelength data sets to compute IR luminosity and then use both (UV and IR) to trace SFR and avoid the underestimation linked to extinction. In chapter.

(6) –5– 2, the UKIDSS data which we used are described, as well as the photometric redshifts, absolute magnitudes and stellar masses, and how they are computed. In chapter 3, the LF is described. In chapter 4, we discuss the comparison of B-band LFs from our sample with previous studies as sanity check of our LF code. In chapter 5, we present the UV LFs. In chapter 6, we present the results of UV LD. In chapter 7, we present the evolution of UV LD with di↵erent stellar masses. Finally, we discuss the implications of our results for the UV LF and UV LD in chapter 8. Throughout this paper, a flat ⇤CDM cosmology is assumed with H0 =70km s. 1. M pc 1 , ⌦⇤ =0.73, and ⌦m =0.27. Unless specified, all magnitudes are in. the AB system (Oke, J.B. 1974)..

(7) –6– 2.. Data. Because galaxies which are reddened by dust or those which appear red due to old stellar populations may be completely missed by standard optical surveys, deep near-IR surveys are crucial for observing high redshift galaxies. In addition, one needs to take advantage of mutiwavelength data to obtain more accurate UV luminosity at high redshift. Hence, we are using the Ultra Deep Survey (UDS) of UKIRT Infrared Deep Sky Survey (UKIDSS) and its mutiwavelength band associated data to obtain the accurate UV luminosity function from low redshift to high redshift. The position of the UDS field is RA(J2000)=02:18:00 and DEC(J2000)=-05:00:00. The UDS DR8 was released worldwide on April 25th 2012. It is the deepest component of the UKIDSS (Lawrence et al., 2007) and it covers 0.8 deg2 . in JHK, up to KAB =24.6, HAB =24.2 and JAB =24.9. Fig. 1-3 shows the field of UKIDSS-UDS. Catalogues were extracted using SExtractor (Bertin & Arnouts 1996), with detections from the K-band image. We excluded the star contamination from catalogues using both compactness criteria and color-color selection of BzK diagram. And we excluded the AGN contamination which is X-ray detected. Because the fraction of obscured AGN is below 15% in total AGN (Gilli et al. 2007). In addition, the UDS field is the Subaru/XMM-Newton Deep Survey covered by very deep Subaru Suprime-cam data (BAB =28.4, VAB =27.8, RAB =27.7, i0AB =27.7 and 0 zAB =26.7, Furusawa et al. 2008), the combination of UDS + SXDS data covers 0.58 deg2 .. Moreover, we also have very deep CFHT Megacam u⇤ -band data observed by a combination of programs lead by O. Almaini and S. Foucaud reaching u⇤AB =27. Given the poorer seeing 00. in u-band (⇠ 1.0 ), it requires PSF corrections to its photometry in order to obtain correct colours for galaxies. The u⇤ -band fluxes were corrected by convolving with the u⇤ -band seeing the B-band image and computing the ratio of counts within apertures between the.

(8) –7– original unsmoothed image and the smoothed image for each source. However the B and u⇤ -band PSFs are not very di↵erent and so the typical correction is less than 1% for this band. Besides, a number of spectroscopic surveys have been conducted on the UDS field, including programmes led by C. Simpson (VLT VIMOS, Simpson et al. 2012), and a campaign of VLT-spectroscopy (VIMOS/FORS2) lead by O. Almaini which has enabled measurements of around 3000 redshifts at z > 1. This is a very helpful for calibrating the photometric redshift estimates. We can compare the UDS with other surveys. The COSMOS field, which aims to study galaxies up to z ⇠ 2 (IAB ⇠ 26) on 2 deg2 has as major advantage the availability of optical HST data. The GOODS-South field, covered by VLT/ISAAC near-infrared imaging, gather an area of 172.5, 159.6 and 173.1 arcmin2 in J, H, and Ks bands, respectively. For point sources total limiting magnitudes of J=25.0, H=24.5, and Ks=24.4 are reached within 75% of the survey area. The FIRES field, it reaches approximately 26.3, 25.8, 25.5 in J, H, and Ks in AB, for a total coverage of about 23.6 arcmin2 . The data we use in the UKIDSS-UDS has the best combination of depth and area coverage, providing a more complete sample to compute luminosity function at faint-end. However, area is still limited and we need to be careful the issue of cosmic variance at bright-end..

(9) –8–. Fig. 1.— The UKIDSS-UDS field. This is a composite image of 3 bands (BzK). Zooming into a small section of the UDS field from K-band image. Light from many of the faint red galaxies has travelled over 12 billion light years to reach our telescopes. The right two fields, represent for the upper one the GOODS-South field, covered with VLT/ISAAC near-infrared imaging on areas of 172.5, 159.6 and 173.1 arcmin2 in J, H, and Ks bands, respectively; and for the lower one the FIRES field, which depths reach approximately 26.3, 25.8, 25.5 in J, H, and Ks, for a total coverage of about 23.6 arcmin2 ..

(10) –9–. Fig. 2.— Location of the UDS field. The UDS field is the Subaru/XMM-Newton Deep Survey field, which lies at the centre of one of the DXS fields, the XMM-LSS field. The UDS field is marked as the small cherry square within the blue DXS square. The dashed line marks the Galactic plane, and the dotted line marks the ecliptic.. Fig.. 3.— UKIDSS-UDS field, x-axis is RA; y-axis is Dec.. The field include the. Subaru/XMM-Newton Deep Survey field, which lies at the centre of one of the DXS fields, the XMM-LSS field. Its total coverage is 0.58 square degree..

(11) – 10 – 2.1.. Photometric Redshifts. The redshift (z) is a crucial information for studying galaxies as it enables the estimation of the distance of galaxies. Because of the expansion of Universe, the faster the object is moving away from us the further it is according to the Hubble’s law, hence, providing a doppler reddening of the spectrum of the galaxy. The most reliable way to estimate z is to use spectroscopy, but it is not a very efficient use of telescope time. Photometric redshifts, obtained by fitting SED on the photometric measurements in di↵erent bands of a given galaxy, is less reliable but much more telescope efficient, enabling to determine redshifts for large galaxy samples. In figure 4, Swindle et al. (2011) present an example of fit of a galaxy SED of galaxy with ugrizYJHK observations (black dash curve) from SDSS and UKIDSS. The redshift, the age of galaxy, stellar mass M⇤ and reddening E(B-V) were derived using from this technique. They used LePhare (Arnouts et al. 1999; Ilbert et al. 2006)1 for a single galaxy in rest-frame with a age fixed to the spectroscopic value of 12.5 Gyr (blue solid curve) and photometrically fit to 2.2 Gyr (red dash-dotted curve). Photometric redshift zphot for our DR8 data were computed by SED fitting using the public EAZY code (Brammer, van Dokkum & Coppi, 2008). It provides very small dispersion with zspec (dispersion is about 0.031, while the outlier fraction is of 3.3%, see Fig.5), therefore it is very useful for our studies. The Fig. 6. shows the redshift distribution of our zphot samples.. 1. http://www.cfht.hawaii.edu/ arnouts/LEPHARE/lephare.html.

(12) – 11 –. Fig. 4.— Example of best-fit SED and bandpasses of filters from Swindle et al. 2011. The black dash curves from left to right are filters in ugrizYJHK (black dash curve), respectively. For a single galaxy in rest-frame with a age fixed to the spectroscopic value of 12.5 Gyr (blue solid curve) and photometrically fit to 2.2 Gyr (red dash-dotted curve)..

(13) – 12 –. Fig. 5.— Comparison of our zphot with zspec . The computation of zphot by SED fitting is from the public EAZY code (Brammer, van Dokkum & Coppi, 2008). Dispersion between zphot and zspec with UKIDSS-UDS DR8 is of ( z/(1 + z)) = 0.031 ,while the outlier fraction is of 3.3% (outside of red line)..

(14) – 13 –. Fig. 6.— The distribution of photometric redshift zphot . Photometric redshift zphot for our DR8 data were computed by SED fitting using the public EAZY code (Brammer, van Dokkum & Coppi, 2008)..

(15) – 14 – 2.2.. Absolute magnitude. The apparent magnitude corresponds to the observed brightness of an object (galaxy, star, etc.), so it is fainter if the object is further, and vice versa. The absolute magnitude corresponds to the intrinsic brightness of objects. It can be derived from the apparent magnitude if we have confirmed the distance of the object, that is to say, the redshift. However, in order to properly derive absolute magnitudes, SED fitting is required. Because the intrinsic SED is shifted via redshift, the flux which we observe is the convolution of shifted SED with observed filter. But the intrinsic flux is from intrinsic SED convolve with rest-frame filter. Therefore, there is a di↵erence that require to correct. This is actually the definition of the k-correction. So fitting SED from the observed bands to determine the intrinsic SED is the most proper way to correct magnitudes. In this work, we derived the rest-frame 1700˚ A absolute magnitude from apparent magnitude of our multiwavlength data. We create a top-hat filter to correspond to the rest-frame 1700˚ A absolute magnitude, the width of filter being 400˚ A (from 1500˚ A to 1900˚ A). To avoid applying huge model-depended corrections, we used our own code to compute the absolute magnitude M for the galaxies from their apparent magnitude m, by using di↵erent bands of DR8 data as a tracer of 1700˚ A rest-frame emission at the mean redshift of the samples. Such as using u-band as tracer of 1700˚ A emission at mean redshift <z>⇠1.2, B-band as tracer at mean redshift <z>⇠1.6, V-band as tracer at mean redshift <z>⇠2 and <z>⇠2.4, r-band as tracer at mean redshift <z>⇠2.8, i-band as tracer at mean redshift <z>⇠3.2. We applied the CWW + KINNEY templates (Coleman et al. 1980, Kinney et al. 1996) to do SED fitting to compute the k-correction K. (See Appendix A1 for more detail.) Then rest-frame 1700˚ A absolute magnitude were computed using the standard relation,.

(16) – 15 – and according to Blanton et al. (2003): M. 1700˚ A. = mobs. 5log(dL /10pc). K. (1). mobs is the apparent magnitude in the observed filter (changing with redshift); dL is the luminosity distance; 5log(dL /10pc) is the distance modulus; K is k-correction. To prevent e↵ect due to the malmquist bias between higher redshift and lower redshift in our redshift bin because the observation limit, we cut the faint limit of M standard distribution for each redshift bin 4z=0.4 as shown in Fig.7.. 1700˚ A. at 3 of.

(17) – 16 –. Fig. 7.— UV 1700˚ A absolute magnitude against photometric redshift. The mean stellar mass is di↵erent at di↵erent redshift because the observing limit. We cut the bright limit of M. 1700˚ A. using a 3 of standard distribution for each redshift bin 4z=0.4. The red dash lines. show the faint limit in each redshift bin..

(18) – 17 – 2.3.. Stellar Mass. In order to have more informations of galaxy evolution, the stellar mass of our DR8 data is also computed from EAZY code. The distribution of stellar mass with photometric redshift is shown in Fig. 8. The mean stellar mass is di↵erent at di↵erent redshift because the observing limit. We cut mass limit at 108.5 M (red dash line) in order to avoid malmquist bias. The red line is our definition for low mass galaxies (M⇤ <1010 M ). The stellar masses used in this work are measured using a multicolour stellar population fitting technique described in Hartley et al. (in prep). We fit the uBVRizJHK bands and IRAC Channels 1 and 2 to a large grid of synthetic spectral energy distributions (SEDs) constructed from the stellar population models of Bruzual & Charlot (2003), assuming a Chabrier initial mass function (G. Chabrier 2003)..

(19) – 18 –. Fig. 8.— The stellar mass which is computed from EZ code, the x-axis is photometric redshift, and y-axis is stellar mass shown in decimal logarithm. The distribution of stellar masses with photometric redshifts is similar than the distribution of absolute magnitudes with photometric redshifts. The mean stellar mass is di↵erent at di↵erent redshift because of observing limits. The red dash line is the mass limit at 108.5 M , and the red line is our definition for low mass galaxies (M⇤ <1010 M ).

(20) – 19 – 3.. Luminosity Function. The luminosity function (LF) is defined as the number of stars or galaxies per luminosity interval. LFs are used to study the properties of large groups or classes of objects, such as the stars in clusters or galaxies. The shape of LF can tell us about the evolution of galaxies, for instance we can see what is the e↵ect by AGNs or supernove from the bright-end slope and faint-end slope of UV LF, as both of AGNs and supernove quench the star formation. For analysis of the evolution of LFs, di↵erent methods can by use to fit and describe the property of galaxies. Nevertheless, the Schechter function (Schechter 1976) is the most common form of LF fitting. We fit it by using a least squares fitting method and obtain the Schechter parameters ↵, M ⇤ and. ⇤. . The M⇤ and. ⇤. are the characteristic. magnitude and number density of a galaxy at the ”knee” of the function, and the ↵ is the faint-end slope of the function. Following is the equation of the Schechter function:. n(L)dL =. ⇤. V (L/L⇤ )↵ exp( L/L⇤ )d(L/L⇤ ).. (2). where the n is number count of galaxies, V is the observable comoving volume and L is luminosity. In this work, we apply the Vmax method (Schmidt 1968) to account for the systematic scattering of galaxies in parameter space. The method does not require any assumptions on the shape of the LF. Owing to its simplicity, this method is the most used in high redshift surveys. Following equations describe the algorithm of Vmax method. The maximum observable comoving volume Vobs,i in which galaxy i can be detected, is given by. Vobs,i =. Z Z !. zmax,i zmin,i. d2 V d!dz. d!dz. (3).

(21) – 20 – The number density. are derived in each absolute magnitude bin k as follows: Ref k dM. =. 1 Vtotal. Ng X Vtotal i=1. Vobs,i. W (MkRef. MiRef ),. where the window function W is defined as, 8 < 1 if dM/2  M Ref k Ref W (Mk M) = : 0 otherwise,. M < dM/2. (4). (5). where Vtotal is the comoving volume between zlow and zhigh . This method can determine the right number from galaxy distribution in the redshift bin. We apply the Poisson counting statistics to estimate the errors of the LF (Marshall 1985), as following: v u Ng uX =t i=1. 1 (Vobs,i. )2. W (MkRef. MiRef ). (6). While we applied a simple estimator for computing LF, Vmax , according to Ilbert et al. (2004), there might be some biases induced using this method for UV LF. In section.6, we will discuss this issue and show the comparison with previous studies, Reddy et al. (2008) and Sawicki et al. (2006), both using Vef f and maximun-likelihood method (STY, SWML)..

(22) – 21 – 4.. B-band Luminosity Function up to z ⇠ 2. As a sanity check, in this section, we compute the rest-frame B-band LFs and compare our results to spectroscopic samples from Ilbert et al. (2005) which is I-band selected sample from VVDS, and from Faber et al. (2007) which is R-band selected sample from DEEP2 and COMBO-17. Ilbert et al. (2005) applied IAB  24.0, corresponding to their limit of the VVDS spectroscopic sample in the VVDS-0226-04 and VVDS-CDFS fields, the sample covering ⇠1750 + 450 arcmin2 . Faber et al. (2007) applied apparent magnitude cuts of RAB  24.1 in their DEEP2 sample and R  24 in COMBO-17 sample, the total sample covering ⇠ 1 deg2 . The di↵erence between these two LFs is because they used di↵erent weights for LF estimate. Ilbert et al. (2005) used wT SR weight. Faber et al. (2007) used optimal weight, minimal weight and average weight. From B-band LF we can explore galaxy evolution of di↵erent epoch. These previous studies found a steepening in faint-end slope for blue galaxies at redshifts beyond z. 0.5,. whereas red galaxies showed little change in either luminosity or number density over the redshift range covered, 0.05  z  1. This implies that red galaxies had formed early before those epochs but that blue galaxies are still evolving. And since the LF of blue galaxies has a steep slope and evolves strongly with redshift (e.g., Lilly et al. 1995; Zucca et al. 2006), the relative contribution of the blue population to the global LF increases with redshift and could explain the steepening of the slope. Fig. 9 shows the LFs at z = 0 ⇠ 2 with a comparison of Ilbert et al. 2005 (red curve) and Faber et al. 2007 (blue curve). Our results are in good agreement with these two previous studies. Although some di↵erences are seen in a few redshift bins, the evolution of the global B-band LF is clearly observed (see Fig.9). It implies that the luminosity contribution is dominated by massive and brighter galaxies at low redshift, then evolved to high redshift, the luminosity dominated by less massive and fainter galaxies. Relative to the.

(23) – 22 – local Schechter function, the galaxies brighten back in time (M⇤B ) but stay roughly constant in number density ( ⇤ ). In short, for the results, galaxies are getting dimmer with time, but their characteristic number density near L⇤ has remained much the same since z⇠1. The faint-end di↵erence between our results and these previous studies is probably due to the method of computing LF: we applied Vmax method, but they applied maximum likelihood method (STY) to correct for missing galaxies. However, given the use of zphot , Vmax based LF with UDS data seems accurate enough..

(24) – 23 –. Fig. 9.— Comparison of B-band LFs with Ilbert et al. 2005 (red curve) and Faber et al. 2007 (blue curve) from z⇠0 to z⇠1.2. The black curve and data points is our results. The x-axis is rest-frame B-band absolute magnitude MB , y-axis is number density . The error of. is shown in Poisson counting statistics..

(25) – 24 – 5.. UV Luminosity Function at z = 1. 3. As we use UV luminosity as SFR tracer, we will probably not account for part of the SFR obscured by dust. However, UV luminosity is still a robust tracer to the SFR as a first step taken for this study. Furthermore, we used NIR selected sample, which should account better for the total number of galaxies, while optically-selected samples will miss all dusty galaxies at high-z. From previous studies we know the peak of SFR is located at z = 1 ⇠ 3 (e.g., Reddy et al. 2008, Cucciati et al. 2012). Therefore, we have focused on our measurements of the UV LF at z ⇠ 1. 3 in this section. The results of rest-frame. 1700˚ A LFs from z⇠1.2 to z⇠3 are shown in Fig.10 & Fig.11. These LFs are computed by using broad range of zphot , and fixed best-fit E(B-V). The Schechter parameters are listed in Table.1. In Fig. 10 & 11, an obvious evolution of rest-frame 1700˚ A LF is observed from higher to lower redshifts, the slope of LF become steeper from z⇠3.2 to z⇠1.2, impling that the luminosity contribution in high redshifts is dominated by massive and bright galaxies, then it evolved to be dominated by less massive and faint galaxies at lower redshift. We realise that the bright-end of the LF is overestimated, and we are still investigating this issue. Our best guess is that these very bright objects have been assigned the wrong zphot by our code, and should be at higher redshift. We plot in Fig. 12 the comparison of UV LF with Reddy et al. 2008 (blue dash curve). Our LFs results at z=1.9⇠2.7 and z=2.7⇠3.4 are consistent with their measurment. They applied Vef f and Maximum likelihood method to compute LF. Their optical images have typical depth of RAB ⇠27.5 from GOODS-North field, HDF-North field and Westphal field, with total area covered almost a square degree. They applied LBG and BX selections, while we selected galaxies from their zphot . These selections use color-color method by dropout technique, and based on their sample selection, they probably missed part of dusty.

(26) – 25 –. Fig. 10.— UV LF from z⇠1.2 to z⇠3.2. The x-axis is redshift, y-axis is rest-frame 1700˚ A absolute magnitude. The error of the standard Schechter function.. is shown in Poisson counting statistics. We do fitting to.

(27) – 26 –. Fig. 11.— Fitting curve of UV LF from z⇠1.2 to z⇠3.2. The x-axis is redshift, y-axis is rest-frame 1700˚ A absolute magnitude. The evolution of rest-frame 1700˚ A LF is observed from z⇠1.2 to z⇠3.2 Table 1: Schechter parameters of UV-LF from z⇠1.2 to z⇠3 Redshift range. M⇤. ⇤. (⇥10 3 ). ↵. 1.0 - 1.4. 18.62+0.1 0.1. 74.7+0.76 0.76. 0.65+0.0038 0.0038. 1.4 - 1.8. 20.05+0.1 0.1. 24.5+0.47 0.47. 1.70+0.0032 0.0032. 1.8 - 2.2. 20.40+0.12 0.12. 10.5+0.21 0.21. 1.44+0.0056 0.0056. 2.2 - 2.6. 20.77+0.12 0.12. 11.4+0.14 0.14. 1.23+0.0068 0.0068. 2.6 - 3.0. 21.05+0.15 0.15. 9.3+0.12 0.12. 1.10+0.0097 0.0097. 3.0 - 3.4. 21.31+0.17 0.17. 7.8+0.09 0.09. 1.03+0.013 0.013.

(28) – 27 – star-forming galaxies in their samples at high redshift. The advantage of our selection is we use deep NIR-seleted samples, enabling a better completeness to study.. Fig. 12.— Comparison of LF results with Reddy et al. (2008) LF at z=1.9⇠2.7 and z=2.7⇠3.4. The upper panel is LF at z=1.9⇠2.7, lower one is LF at z=2.7⇠3.4. The blue dash curve is from Reddy et al. (2008) and black curve is our results. The error of. is. shown in Poisson counting statistics. Fig.13 shows our results against Sawicki et al. 2006 (red dash curve). Their LFs at z⇠1.7, z⇠2.3 and z⇠3 are computed with Vef f method and their samples are R-band selected (RAB ⇠27) from very deep Un GRI Keck imaging survey. It covers a total area of 169 arcmin2 . As Reddy et al. (2008), they applied BX and LBG sample. Although they have wider observing area than our data, we have more complete sample to compute LF. The methods of computing LF play a important role in this di↵erence of UV LF.

(29) – 28 –. Fig. 13.— Comparison of LF results with Sawick et al. (2006) at z⇠1.7, z⇠2.3 and z⇠3. The dash red curve is from Sawicki et al. (2006) and black curve is our result. The error of is shown in Poisson counting statistics..

(30) – 29 – between our results and Reddy et al. (2008)/Sawick et al. (2006). According to Ilbert et al. (2004), they mentioned that the underestimate may be particularly significant for Vmax method. Also, as shown in Figure 10, Figure 12 and Figure 13, we can not fit well for the bright-end od LF due to a contamination of high-z faint galaxies assigned by our Zphot code to lower-z galaxies..

(31) – 30 – 6.. UV Luminosity Density at z=1-3. The UV luminosity density provides an estimate of the total amount of light emitted by galaxies per unit volume. In the present work we compute the UV luminosity density assuming the Schechter form of the luminosity function (Schechter 1976). Once we have the Schechter parameters ↵, M⇤ and. ⇤. , we can derive the UV luminosity density, by integrating. it from the observed bright-end to a fixed faint-end. (Llim =L⇤z=0 , where L⇤z=0 is the L⇤ at z=0.) Fig.14 presents the evolution in the integrated Schechter fit LD from our sample, compared with previous studies. Our errors are standard errors from the fitting procedure. We compare our results with a compilation from Cucciati et al. (2012), Reddy et al. (2008) and Bouwens et al. (2007). The results of LD from z⇠1 to z⇠3 are consistent with Reddy et al. (2008) and Cucciati et al. (2012). Our results are done for smaller bins compared to previous studies of redshift. The evolution of UV LD from z ⇠ 3 to z ⇠ 1 is a good representation of the evolution of SFR and agrees well with previous studies (Reddy et al. 2008, Bouwens et al. 2007, Cucciati et al. 2012). Cucciati et al. (2012) use both the Deep and Ultra-Deep surveys obtained in the VVDS-0226-04 field with spectroscopy redshift, over 2200 arcmin2 of sky area. The depth of data is IAB  24.75; Reddy et al (2008), used optical data from LBG selection with typical depth of RAB ⇠27.5 from GOODS-North field, HDF-North field and Westphal field, total area covered almost a square degree; Bouwens et al. (2007), used a high-redshift LBG sample from HUDF, HUDF-Ps, HUDF05, and GOODS fields, with detecting limits i775,AB > 26.5 (GOODS), i775,AB > 27.3 ( HUDF-Ps/ HUDF05 ), and i775,AB > 28 ( HUDF ), for a total coverage of about 400 arcmin2 . Thanks to our large sample, we can reduce the size of the redshift bins and have consistent method to compare to these previous studies. Because our data is deeper, we.

(32) – 31 – should have better faint-end result. However, the area of other studies can be wider than our, meaning their bright-end should be less biased. Nevertheless, these results present evidences that the UV LD peak at z ⇠2 (Fig.14). After an increase from z⇠6 to z⇠2, the UV LD decreases sharply down to z⇠0. It tells us the galaxies number increase very fast in early universe, then the speed of increasing slow down from z⇠ 2. There are two explanation in recent scenario of galaxy evolution from these results: First, the e↵ect of kinetical feedback, we think it is because of gas exhaustion (Tresse et al. 2007) or truncation of the star formation such as through AGN or supernova feedback (e.g., Kriek et al. 2006; Reddy et al. 2006b, 2005; Erb et al. 2006c); In the other hand, the e↵ect of thermal feedback tell us due to heating by some mechanisms gas is unable to cool in galaxies with the largest stellar masses. This includes AGN feedback (Scannapieco et al. 2005; Granato et al. 2004) and dilution of infalling gas due to virial shock ( Dekel & Birnboim 2006). Interestingly, it is around this epoch, z ⇠ 2, that AGN activity appears to peak making AGN feedback a good candidate as potential mechanisms of star formation quenching. (e.g., Hopkins et al. 2007; Fan et al. 2001; Shaver et al. 1996). In order to better constrain these scenario and have a better understanding of galaxy evolution, we can use our results and compare to di↵erent properties of galaxies. One possible way is to explore LD in di↵erent stellar mass with redshifts, which is done in next section..

(33) – 32 –. Fig. 14.— LD evolution for our data (in red crosses) compared with Reddy et al. (2008) at z⇠2. 3 (blue diamons), Cucciati et al. (2012) at z = 0.3-3.0 (black squares) and Bouwens. et al. (2007) at z = 4-6 (green triangles).

(34) – 33 – 7.. Luminosity Density of Low Stellar Mass System. Thanks to the stellar mass we derived by SED fitting, we select low stellar mass galaxies with 108.5 M < M⇤ <1010 M to compute their LD. Compare to LD of full sample (M⇤ >108.5 M ), we explore preliminarily the contribution of LD from low mass system to total LD. In order to have more obvious trend, we use smaller redshift bins instead of. z=0.2. z=0.4 in 1< z <1.8. We also select sample only in redshift range 1< z <2 to. avoid malmquist bias at z> 2 (see Fig.8). Our results are in Fig.15, we observe a slight increase of this ratio from high redshift to low redshift. The measurement at z⇠1.7 is surprising low and we guess it is due to a combination of problems of our bright-end and a possible structure at this redshift (see Fig.6). If this structure is real, we are actually expecting a drop of the LD in low mass galaxies due to environment e↵ects. We ignore this measurement when we describe the trend of the ratio evolution. This trend means the LD contribution is dominated by low mass galaxies at low redshift, and higher mass galaxies at high redshift. This is the actually consistent with downsizing scenario, which tells us the locus of SFR migrate from high mass galaxies at high redshift to low mass galaxies at low redshift. Of course due to unaccounted extinction we can’t derive directly the e↵ect on SFR..

(35) – 34 –. Fig. 15.— The fraction of luminosity density of low mass system and total luminosity density.

(36) – 35 – 8.. Conclusion and Summary. The UDS is currently the deepest and most extensive infrared survey ever conducted of the distant Universe. Furthermore, our K-selected study is less biased against dusty galaxies unlike previous I-band or R-band selected studies. We have used the DR8 photometry in combination with CFHT u⇤ -band and SXDS optical data to derive the 1700˚ A absolute magnitude. Our LF results shown in section 5 are in good agreements with previous studies (Reddy et al. 2008, Sawicki et al. 2006). The bright-end slope of the LF become steeper from high redshift to low redshift, and M ⇤ become fainter from high redshift to low redshift. Also our UV LD which is a good indicator of SFR agrees very well with previous studies at z > 2 (see Figure 14), also we can better constrain the UV LD because our smaller redshift bin. We confirm that the peak of UV LD is at z⇠2, which implies that star-forming galaxies are forming more actively stars at that epoch, and we can better constrain the UV LD because our smaller redshift bin. We compute the ratio between LD of low stellar mass as 108.5 M < M⇤ <1010 M and LD of full sample (M⇤ >108.5 M ) with redshifts. We derive a preliminary result on the contribution of LD from low mass system to total LD (Fig.15). We show a trend from lower ratio at high redshift then increase to higher ratio at low redshift. All these results indicate UV luminosity is dominated by low mass system at low redshift and high mass at system. This is the actually evidence of downsizing scenario, which tells us the SFR dominated by massive system at high redshift but dominated by less mass system. To explain this trend in individual galaxy, we guess the most luminous and massive galaxies have exhausted their cold gas reservoir during their early intense star formation.

(37) – 36 – which has occured in the early universe, they undergo passive evolution as star formation cease. At z ⇠ 2, AGN activity appears to peak (e.g., Hopkins et al. 2007; Fan et al. 2001; Shaver et al. 1996) indicating a relation between AGN and evolution of SFR. As highlighted previously, UV LD is a direct tracer of SFR, but a fraction of luminosity is missed due to dust extinction. Consequently, the proper way is that we have to observe the IR luminosity and combine UV and IR to trace the SFR. Herschel and 24um MIPS data are available on the UDS field, and we are planning to use them to IR LD, then we can bring much better constrain on the star-formation rate history..

(38) – 37 – 9.. Reference. Arnouts et al. 1999, M N RAS, 310, 540 Bertin & Arnouts 1996, A&A Supplement, 317, 393 Blanton et al. 2003a, AJ, 125, 2348 Bouwens et al. 2007, ApJ, 670, 928 Caputi et al. 2007, ApJ, 660, 97 Coleman et al. 1980, ApJS, 43, 393 Cowie et al. 1996, AJ, 112, 839 Cucciati et al. 2012, A&A, 539, A31 Dekel & Birnboim 2006, M N RAS, 368, 2 Erb et al. 2006c, ApJ, 646, 107 Faber et al. 2007, ApJ, 665, 265 Fan et al. 2001, AJ, 122, 2833 Furusawa et al. 2008, ApJS, 176, 1 Gilli et al. 2007, A&A, 463, 79 Granato et al. 2004, ApJ, 600, 580 Hartley et al. (in prep) Hirashita et al. 2003, A&A, 410, 83 Hopkins et al. 2006, ApJ, 652, 107 Hopkins et al. 2007, ApJ, 654, 731.

(39) – 38 – Ilbert et al. 2004, M N RAS, 351, 541 Ilbert et al. 2005, A&A, 439, 863 Kinney et al. 1996, ApJ, 467, 38 Kriek et al. 2006, ApJ, 649L, 71 Lawrence et al. 2007, MNRAS, 379 ,1599 Lehmer et al. 2008, ApJ, 681, 1163 Lilly et al. 1995, ApJ, 455, 108 Marshall 1985, ApJ, 289, 457 Norman et al. 2004, ApJ, 607, 721 Oesch et al. 2010, AP J, 725, 150 Oke, J.B. 1974, ApJS, 27, 21 P` erez-Gonz`alez et al. 2005, ApJ, 630, 82 Quadri et al. 2012, ApJ, 744, 88 Reddy et al. 2008, ApJS ,175, 48 Sawicki et al. 2005, ApJ, 635, 100 Sawicki et al. 2006, ApJ, 642, 653 Scannapieco et al. 2005, ApJ, 635, 13 Schechter 1976, ApJ, 203, 297 Schiminovich et al. 2005, ApJ, 619, 47 Shaver et al. 1996, N ature, 384, 439.

(40) – 39 – Simpson et al., 2012, M N RAS, 421, 3060 Steidel et al. 2004, ApJ, 604, 534 Swindle et al. 2011, AJ, 142, 118 Tresse et al. 2002, M N RAS, 337, 369 Tresse et al. 2007, A&A, 472, 403 Zucca et al. 2006, A&A, 455, 879.

(41) – 40 – Appendix A1. To check our calculation for absolute magnitude, we used mock catalogs from Henriques et al. (2012) computed from the semi-analytic modelling (SAM) of galaxy formation based on Millennium N-body simulation. The aim of this work is aim to predict the evolution of population properties, including the distributions of stellar mass, luminosity, star formation rate, size, rotation velocity, morphology, gas content and metallicity, as well as the scaling relations linking these properties. The data set includes redshifts, apparent magnitudes with di↵erent filters, and rest-frame absolute magnitudes with di↵erent colors, etc,. In order to determine the absolute magnitude, we use CWW + KINNEY templates (Coleman et al. 1980, Kinney et al. 1996) to do SED fitting to derive k-correction. We applied the same method than our data. In addition, we don’t use only one band to trace the intrinsic magnitude because it will be model dependent. We use di↵erent band with redshift instead. Since it is simulation, we know the intrinsic rest-frame absolute magnitude. We use it to check how good is our calculation by di↵erencing between our results and the given absolute magnitude. Our UV-LF is computed in a mock top-hat filter at 1700˚ A filter with 400˚ A width. For every galaxy, first we shift at each SED template to the observed-frame according to its redshift, then we convolve the SED by all uBVRizJHK filters to get magnitudes. In addition, we adjust SED in the flux direct to identify its proper scale. Then we use chi-square minimisation to find the best SED template. We convolve intrinsic SED with 1700˚ A filter to get the intrinsic magnitudes. Finally, we can get the k-correction by computing the di↵erence between the magnitude from shifted SED and the intrinsic magnitude from intrinsic SED. Fig.16 shows the dispersion of our computed absolute magnitudes and the absolute.

(42) – 41 – magnitudes given by the Mock, we get a dispersion of the order of 1 mag. And we show the dispersion with redshift in Fig.17, the black points are computed absolute magnitude before k-correction, red points are absolute magnitude after k-correction. This 1 magnitude dispersion cannot a↵ect LF a lot. It tell us that our calculation doing well.. Fig. 16.— The dispersion between our computing absolute magnitude and given absolute magnitude..

(43) – 42 –. Fig. 17.— The dispersion between our computing absolute magnitude and given absolute magnitude with redshift. The black points are computed absolute magnitude before kcorrection, red points are absolute magnitude after k-correction..

(44) - 43 -. Appendix A2. Following is our idl code for computing LF: pro plotlf_v, z, mab,sh=sh,ldd=ldd,phi=phi,er=er,x=x, $ bin=bin,sh_init=sh_init,fitn=fitn,area=area,ftend=ftend, $ cucciati12=cucciati12,oesch10=oesch10,reddy08=reddy08,sawicki06=sawicki06 ;Input: ;mab:absolute magnitude(array), ;z:redshift with mab(array), ;optional input: ;area: fov (default:0.58 for UDS) ;/cu,/oesch,/reddy,sawicki: comparison ;sh_init: suggustion for schecter parameter ;bin:magnitude bin (e.g. bin=0.5 or bin=0.25 ...;default: 0.5) ;fitn=decreasing data number after cut for schecter function fitting (default:0) ; ;Output: ;sh: schecter parameter---phi*,M*,alpha, phi_e,M_e,alpha_e ;ldd: luminosity density ;phi ;er: error of phi ;x: mag bin nn=n_elements(z) zr=(max(z)+min(z))/2d a=0.58 ;UKIDSS UDS: UKIRT+SUBARU IF n_elements(area) ne 0 THEN a=area IF n_elements(bin) eq 0 THEN bin=0.5 IF n_elements(ftend) eq 0 THEN ftend=-18. rr=fltarr(100000) phi=fltarr(14d/bin+1) er=fltarr(14d/bin+1) x=fltarr(14d/bin+1) for i=0,14d/bin do begin rr=where(mab ge i*bin+min(mab) and mab lt (i+1)*bin+min(mab),cn) if rr[0] ne -1 then begin phi[i]=(1d/bin)*total(1d/ajs_comvol(z[rr],area=a)) er[i]=phi[i]/sqrt(cn) ;(1d/bin)*sqrt(total(1d/(ajs_comvol(z[rr],area=a))^2)).

(45) - 44 x[i]=min(mab)+(i+0.5)*bin endif endfor z_r=round(zr*10)*0.1 IF n_elements(ftend) eq 0 THEN $ ;decide the faint end for plot fd=-18 IF n_elements(ftend) ne 0 THEN $ fd=ftend plot, x,phi,xrange=[-24,fd],yrange=[0.0000001,0.1] $ ,/ylog,xtitle = 'M - 5log h',ytitle = ' !4U!3 / (h!U3!N Mpc!U-3!N dex!U-1!N) ' $ ,title=z_r,psym=3,LINESTYLE=6,color=fsc_color("Black"),background=fsc_color('white') errplot,x,phi-er,phi+er,color=fsc_color('Black') o=where(phi ne 0 and x le 0,c) x=x[o] phi=phi[o] ua=phi[0:c-1]-phi[1:c-2] ub=where(ua le 0,cc) IF n_elements(fitn) ne 0 THEN ub=[ub,max(ub)+fitn] x1=x[ub] phi1=phi[ub] er1=er[ub] IF n_elements(sh_init) ne 0 THEN $ schechter={phistar:sh_init[2], mstar:sh_init[0], alpha:sh_init[1], $ phistar_err:0.d, mstar_err:0.d, alpha_err:0.d} IF n_elements(sh_init) ne 0 THEN $ lf_fit_schechter, x1,phi1,er1,schechter ;sh_init---phi,M,alpha IF n_elements(sh_init) ne 0 THEN $ sh=schechter lf_fit_schechter, x1,phi1,er1,sh ;sh_init=[M*,alpha,phi*] ;IF n_elements(sh_init) EQ 0 THEN $ ; sh=ajs_schechter_fit(x1,phi1,er1, range=[round(max(mab)),round(min(mab))] ) ; sh=ajs_schechter_fit(x1,phi1,er1,range=[round(max(mab)),round(min(mab))],params_init= sh_init) ;IF n_elements(ftend) eq 0 THEN $ s=[-24,-23.5,-23,-22.5,-22,-21.5,-21,-20.5,-20,-19.5,-19,-18.5,-18,-17.5,-17,-16.5,-16] IF ftend eq -14 THEN $ s=[s,-15.5,-15,-14.5,-14].

(46) - 45 IF ftend eq -12 THEN $ s=[s,-15.5,-15,-14.5,-14,-13.5,-13,-12.5,-12] ;oplot,s,lf_schechter(s,sh[2],sh[0],sh[1]),color=fsc_color('White') ;ldd=1e7*ld(sh[0],sh[2],sh[1]) oplot,s,lf_schechter(s,sh.(0),sh.(1),sh.(2)),color=fsc_color('White') ldd=1e7*ld(sh.mstar,sh.phistar,sh.alpha) print,'total number=',nn print,'phi*_(10^-3)=',sh.phistar*1000d;sh[2]*1000d print,'M*=',sh.mstar;sh[0] print,'Alpha=',sh.alpha;sh[1] print,'total luminosity density=',ldd print,'redshift~',z_r ;legend,['This work','Reddy08','Sawicki06'],psym=[0,0,0],box=0,linestyle=[0,0,0],color=['FFFFFF'x, 255,'00FF00'x],/bottom,/right if keyword_set(oesch10) then begin legend,['This work','Oesch et al. 2010'],charsize=2,box=0,linestyle=[0,2],$ textcolors=[fsc_color('White'),fsc_color('Green')],$ color=[fsc_color('White'),fsc_color('Green')],/bottom,/right case 1 of ;Oesch10 (green line) (z_r gt 1) and (z_r le 1.3) :begin oplot,s,lf_schechter(s,1/(10^2.9),-20.08,-1.84),color=fsc_color('Green'),linestyle=2 end (z_r gt 1.3) and (z_r le 1.7) :begin oplot,s,lf_schechter(s,1/(10^2.64),-19.82,-1.46),color=fsc_color('Green'),linestyle=2 end (z_r gt 1.7) and (z_r le 2.1) :begin oplot,s,lf_schechter(s,1/(10^2.66),-20.16,-1.6),color=fsc_color('Green'),linestyle=2 end (z_r gt 2.1) and (z_r le 2.7) :begin oplot,s,lf_schechter(s,1/(10^2.49),-20.69,-1.73),color=fsc_color('Green'),linestyle=2 end else : print,'no comparison' endcase endif if keyword_set(sawicki06) then begin legend,['This work','Sawicki et al. 2006'],charsize=2,box=0,linestyle=[0,2],$ textcolors=[fsc_color('White'),fsc_color('Red')],$ color=[fsc_color('White'),fsc_color('Red')],/bottom,/right case 1 of ;Sawicki06 (red line) (zr gt 1.5) and (zr le 1.9) :begin oplot,s,lf_schechter(s,1/(10^1.77),-19.8,-0.81),color=fsc_color('Red'),linestyle=2.

(47) - 46 end (zr gt 1.9) and (zr le 2.5) :begin oplot,s,lf_schechter(s,1/(10^2.52),-20.6,-1.20),color=fsc_color('Red'),linestyle=2 end (zr gt 2.5) and (zr le 3.5) :begin oplot,s,lf_schechter(s,1/(10^2.77),-20.9,-1.43),color=fsc_color('Red'),linestyle=2 end (zr gt 3.5) and (zr le 4.5) :begin oplot,s,lf_schechter(s,1/(10^3.07),-21.0,-1.26),color=fsc_color('Red'),linestyle=2 end else : print,'no comparison' endcase endif if keyword_set(reddy08) then begin legend,['This work','Reddy et al. 2008'],charsize=2,box=0,linestyle=[0,2],$ textcolors=[fsc_color('White'),fsc_color('Blue')],$ color=[fsc_color('White'),fsc_color('Blue')],/bottom,/right case 1 of ;reddy08 (blue line) (zr gt 1.9) and (zr le 2.7) :begin oplot,s,lf_schechter(s,0.00162,-21.01,-1.88),color=fsc_color('Blue'),linestyle=2 ;nd=1e7*ld(-21.01,0.00162,-1.88) ;print, 'nd=',nd end (zr gt 2.7) and (zr le 3.4) :begin oplot,s,lf_schechter(s,0.00112,-21.12,-1.85),color=fsc_color('Blue'),linestyle=2 end else : print,'no comparison' endcase endif if keyword_set(cucciati12) then begin legend,['This work','Cucciati et al. 2012'],charsize=2,box=0,linestyle=[0,2],$ textcolors=[fsc_color('White'),fsc_color('Gold')],$ color=[fsc_color('White'),fsc_color('Gold')],/bottom,/right case 1 of ;Cucciati 12 (zr gt 0.05) and (zr le 0.2) :begin oplot,s,lf_schechter(s,0.007,-18.12,-1.05),color=fsc_color("Gold"),linestyle=2 end (zr gt 1) and (zr le 1.2) :begin oplot,s,lf_schechter(s,0.00743,-19,-1.2),color=fsc_color("Gold"),linestyle=2 end (zr gt 1.2) and (zr le 1.7) :begin oplot,s,lf_schechter(s,0.0041,-19.6,-1.09),color=fsc_color("Gold"),linestyle=2 end (zr gt 1.7) and (zr le 2.5) :begin oplot,s,lf_schechter(s,0.00337,-20.4,-1.3),color=fsc_color("Gold"),linestyle=2.

(48) - 47 end (zr gt 2.5) and (zr le 3.5) :begin oplot,s,lf_schechter(s,0.00086,-21.4,-1.5),color=fsc_color("Gold"),linestyle=2 end else : print,'no comparison' endcase endif ;;B-band ;(zr gt 0.8) and (zr le 1) : begin ;;Ilbert_05,~0.9 ;oplot,s,lf_schechter(s,0.00907,-20.87,-1.33),color=fsc_color('Red') ;;Faber_07,~0.9 ;oplot,s,lf_schechter(s,0.004126,-21.25,-1.3),COLOR=fsc_color('Blue') ;end ; ;(zr gt 0.4) and (zr le 0.6) : begin ;;Ilbert_05,~0.5 ;oplot,s,lf_schechter(s,0.00962,-20.45,-1.22),color=fsc_color('Red') ;;Faber_07,~0.5 ;oplot,s,lf_schechter(s,0.003332,-21.2,-1.3),COLOR=fsc_color('Blue') ;end ; ;(zr gt 0.6) and (zr le 0.8) :begin ;;Ilbert_05,~0.7 ;oplot,s,lf_schechter(s,0.01507,-20.36,-1.12),color=fsc_color('Red') ;;Faber_07_combo17,~0.7 ;oplot,s,lf_schechter(s,0.003216,-21.52,-1.3),COLOR=fsc_color('Blue') ;end ; ;(zr gt 0.2) and (zr le 0.4) :begin ;;Ilbert_05,~0.3 ;oplot,s,lf_schechter(s,0.0146,-20.09,-1.15),color=fsc_color('Red') ;;Faber_07_combo17,~0.3 ;oplot,s,lf_schechter(s,0.003226,-21.00,-1.3),COLOR=fsc_color('Blue') ;end ; ;(zr gt 1) and (zr le 1.2) :begin ;;Ilbert_05,~1.1 ;oplot,s,lf_schechter(s,0.0162,-20.7,-1.33),color=fsc_color('Red') ;;Faber_07_combo17,~1.1 ;oplot,s,lf_schechter(s,0.003472,-21.38,-1.3),COLOR=fsc_color('Blue') ;end ; ;(zr gt 0) and (zr le 0.2) :begin ;;Ilbert_05,~0.1 ;oplot,s,lf_schechter(s,0.02119,-19.39,-1.09),color=fsc_color('Red') ;end end.

(49) - 48 -. Appendix A3. Following is our idl code for computing k-correction: pro kc_fit, z, u=u,bd=bd,v=v,r=r,i=i,zm=zm,j=j,h=h,kb=kb,kcn=kcn,chi2=chi2,band=band,sedn=sedn,ap m=apm ;purpose: find best sed then do convlution with filter to get rest-frame mag ; ;INPUT ; z: redshift ; u~k: each color, apparent mag ; band: use 'uv' or 'u' or 'b'... to select which band in rest-frame ; ; ;OUTPUT ; amag: rest-frame apparent mag ; chi2: chisquare from best SED. ;-------------------------------------------------------------------------;-------------------------start time-------------------t1=systime(/seconds) ;set start for calculating how much time it spend ;-------------------------------------------------------------------------;-------------------------------------------------------------------------;make gallaxy's all bands data n=n_elements(z) kcn=dblarr(n) chi2=dblarr(n) sedn=dblarr(n) print,'total galaxies:',n for x=0,n-1 do begin ;-------------------------------------------------------------------------;-------------------------start time-------------------t01=systime(/seconds) ;-------------------------------------------------------------------------;-------------------------------------------------------------------------obs_data=[u[x],bd[x],v[x],r[x],i[x],zm[x],j[x],h[x],kb[x]] ;find best fit SED by min chi2 minchi2, obs_data,z=z[x],mincs=chisq,scale=ss, fitsed=sedx chi2[x]=chisq.

(50) - 49 if sedx eq 'sed1' then sedn[x]=1 if sedx eq 'sed2' then sedn[x]=2 if sedx eq 'sed3' then sedn[x]=3 if sedx eq 'sed4' then sedn[x]=4 if sedx eq 'sed5' then sedn[x]=5 if sedx eq 'sed6' then sedn[x]=6 if sedx eq 'sedc' then sedn[x]=7 if sedx eq 'sedd' then sedn[x]=8 if sedx eq 'sede' then sedn[x]=9 if sedx eq 'sedi' then sedn[x]=10 ;obs-frame convlution mag from SED upd=dblarr(13) zpmag=dblarr(13) for ted=0,12 do begin upd[ted]=ted-5 cvlm_uv, ssed=sedx, cm=cm2,z=z[x],updown=upd[ted] bandtol = { uv:[170], u:[350], b:[436.641],v:[542.956],r:[622.057],i:[764.124],zm:[914.674],j: [1252.9],h:[1642.69],k:[2228.63],m36:[3600],m45:[4500] } tag = tag_names(bandtol) tag1 = strupcase(band) op = where(tag eq tag1) value=(bandtol.(op)*(1+z[x])) if (value gt 150) and (value le 190 ) then zpmag[ted]=cm2[0] if (value gt 300) and (value le 400 ) then zpmag[ted]=cm2[1] if (value gt 400) and (value le 500 ) then zpmag[ted]=cm2[2] if (value gt 500) and (value le 583) then zpmag[ted]=cm2[3] if (value gt 583) and (value le 690 ) then zpmag[ted]=cm2[4] if (value gt 690) and (value le 820 ) then zpmag[ted]=cm2[5] if (value gt 820) and (value le 1000) then zpmag[ted]=cm2[6] if (value gt 1000) and (value le 1450) then zpmag[ted]=cm2[7] if (value gt 1450) and (value le 1900) then zpmag[ted]=cm2[8] if (value gt 1900) and (value le 2400) then zpmag[ted]=cm2[9] endfor best=upd[where(abs(apm[x]-zpmag) eq min(abs(apm[x]-zpmag)))] zpmag1=zpmag[where(abs(apm[x]-zpmag) eq min(abs(apm[x]-zpmag)))] ;to avoid infinity ...but seems no work if best eq -5 then best=-5 if best eq -4 then best=-4 if best eq -3 then best=-3 if best eq -2 then best=-2 if best eq -1 then best=-1 if best eq 0 then best=0 if best eq 1 then best=1 if best eq 2 then best=2 if best eq 3 then best=3 if best eq 4 then best=4 if best eq 5 then best=5 if best eq 6 then best=6.

(51) - 50 if best eq 7 then best=7 ;rest-frame convlution mag from SED cvlm_uv, ssed=sedx, cm=cm1 ,updown=best ; to avoid infinity if cm1[1] gt 100 then cvlm, ssed=sedx, cm=cm1 ;choose which band in rest-frame if strupcase(band) eq strupcase('uv') then pmag=cm1[0] if strupcase(band) eq strupcase('u') then pmag=cm1[1] if strupcase(band) eq strupcase('b') then pmag=cm1[2] if strupcase(band) eq strupcase('v') then pmag=cm1[3] if strupcase(band) eq strupcase('r') then pmag=cm1[4] if strupcase(band) eq strupcase('i') then pmag=cm1[5] if strupcase(band) eq strupcase('zm') then pmag=cm1[6] if strupcase(band) eq strupcase('j') then pmag=cm1[7] if strupcase(band) eq strupcase('h') then pmag=cm1[8] if strupcase(band) eq strupcase('k') then pmag=cm1[9] ;k-correction value = rest-frame mag - obs-frame mag kcn[x]=pmag-zpmag1 ;-------------------------------------------------------------------------;----------------------------calculate time------------t02=systime(/seconds) t0=(t02-t01)*(n-x) hr=fix(t0/3600d) mint=fix( (t0-(hr*3600d))/60d ) sec=t0-hr*3600d -mint*60d ;print,'left:',n-x-1 if (fix(x/10d)-x/10d) eq 0 then print,'waiting for',hr,'hour',mint,'min',sec,'sec' ;-------------------------------------------------------------------------;-------------------------------------------------------------------------endfor kcn=kcn ;-------------------------------------------------------------------------;----------------------------calculate time------------t2=systime(/seconds) hour=fix((t2-t1)/3600d) minute=fix(((t2-t1)-hour*3600d)/60) sec=(t2-t1)-hour*3600d - minute*60d print,'total time is',minute,'min',sec,'sec' ;-------------------------------------------------------------------------;-------------------------------------------------------------------------end.

(52) - 51 -. pro dr8kc, z1,z2 ,name,rest=rest ;run SED fitting for k-correction vi mobile phone restore,'dr8n.sav' if n_elements(z1) eq 0 then z1=min(z) if n_elements(z2) eq 0 then z2=max(z) aa=where(z gt z1 and z le z2 and u le 40 and b le 40 and v le 40 and r le 40 and i le 40 and zm le 40 and j le 40 and h le 40 and k le 24.6) zp=z[aa] u=u[aa] b=b[aa] v=v[aa] r=r[aa] i=i[aa] zm=zm[aa] j=j[aa] h=h[aa] kb=k[aa] u17=u17[aa] mass=mass[aa] band='uv' ;if n_elements(rest) ne 0 then band=rest gtreb ,rtf=band,zp,u,b,v,r,i,zm,j,h,kb,apm=apm kc_fit, zp, u=u,bd=b,v=v,r=r,i=i,zm=zm,j=j,h=h,kb=kb,chi2=chi2,band=rest ,kcn=kcn,apm=apm. abmag=gtabs(apm+kcn,zp,o_m=0.25,o_l=0.75,H0=73) if n_elements(name) eq 0 then name='temp.sav' save,/all,filename=name exit end.

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