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# The Effect of a Sexual Health Promotion Training Program on Sexual Function of Pregnant Women with Gestational Diabetes Mellitus

AUTHORS

Elahe Fayyazian 1 , Farnoosh Khojasteh 2 , * , Farshid Saeedinezhad 3 , Maryam Haghighi 4

1 School of Nursing and Midwifery, Zahedan University of Medical Sciences, Zahedan, Iran

2 Pregnancy Health Research Center, Zahedan University of Medical Sciences, Zahedan, Iran

3 Community Nursing Research Center, Zahedan University of Medical Sciences, Zahedan, Iran

4 Anesthesia Department, Paramedical School, Zahedan University of Medical Sciences, Zahedan, Iran

How to Cite: Fayyazian E, Khojasteh F, Saeedinezhad F, Haghighi M. The Effect of a Sexual Health Promotion Training Program on Sexual Function of Pregnant Women with Gestational Diabetes Mellitus. Med Surg Nurs J. 2021;10(1):e118769. doi: 10.5812/msnj.118769.

ARTICLE INFORMATION

Medical - Surgical Nursing Journal: 10 (1); e118769
Published Online: August 28, 2021
Article Type: Research Article
Accepted: August 15, 2021
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### Abstract

Background: Pregnancy care and screening programs are very important, especially in high-risk pregnancies. However, few interventional studies have addressed mental and sexual health in women with gestational diabetes mellitus (GDM).

Objectives: The present study aimed to examine the effect of a sexual health promotion training program on sexual function of pregnant women with GDM referring to comprehensive health centers in Zahedan, Iran, in 2020.

Methods: This quasi-experimental study was performed on 80 pregnant women with GDM (gestational age: 24 - 30 weeks). The participants were selected using multi-stage sampling method and randomly assigned into intervention and control groups. The participants in the intervention group received sexual health promotion training in four sessions (60 - 90 minutes) two sessions per week. The participants in the control group received routine care. The demographic information questionnaire was completed by the participants at the beginning of the study, and the Female Sexual Function Index (FSFI) was administered before and four weeks after the completion of the sexual health promotion training program. The collected data were analyzed in SPSS software (version 22) using independent samples t-test, paired samples t-test, analysis of covariance (ANCOVA), and chi-square test.

Results: The results showed a statistically significant difference between the intervention and control groups in all subscales of sexual function (P < 0.05). Moreover, the results of ANCOVA for the total sexual function score showed that the women in the intervention group had significantly higher levels of sexual function (22.89 ± 3.24) compared to the women in the control group (16.78 ± 3.16) (P = 0.001).

Conclusions: Given the positive and significant effect of sexual health promotion training on the sexual function of pregnant women with GDM, it is recommended to integrate this training program in prenatal care of these vulnerable women.

Keywords

### 1. Background

Pregnancy is one of the most challenging psychological events in women’s life that can have positive and negative effects in the long run (1). During this period, the woman’s body undergoes anatomical and physiological changes for fetal growth, metabolic needs, and readiness for delivery (2). Pregnant women frequently experience physiological and metabolic changes that affect different systems in their body organs (3). Since the mother’s cardiovascular, pulmonary, immune, and metabolic systems are altered during pregnancy, maladjustment of the mother’s physiology during this period may cause abnormal birth weight or gestational diabetes mellitus (GDM) (4).

GDM is defined as the degree of blood sugar that is a metabolic disorder with first recognition during pregnancy and includes type 2 diabetes that has not been previously diagnosed and GDM that develops later in pregnancy (5). The World Health Organization (WHO) defines GDM as glucose intolerance of variable degree (6). Blood sugar is normal if the fasting blood sugar level is less than 92 and the blood sugar two hours after the meal is less than 153, but if any of them is equal to or higher than these levels, it is considered GDM (7), which is diagnosed in the second or third trimester (8).

GDM is currently the most common complication of pregnancy (5). However, its prevalence varies in different parts of the world, and the possible causes of this variation are unknown with no precise spatial classification. Nevertheless, the available data indicate that GDM is prevalent in 14% of pregnancies worldwide, accounting for approximately 18 million annual births (9). According to the estimations, 16.9% of all pregnancies worldwide (10) and 17% of all pregnancies in Iran are associated with GDM (11). Diabetes in the sensitive period of pregnancy has profound effects on the internal environment of the uterus and may impair fetal or maternal function (12).

One of the most serious complications of GDM is a decrease in sexual function. This metabolic disorder not only can cause neurovascular injury, but also have psychological damages (13). The prevalence of sexual dysfunction in people with diabetes is about three times higher than in the general population (14). The WHO defines sexual health as a state of physical, emotional, mental, and social well-being in relation to sexuality (15). Sexual function plays an essential role in marital satisfaction. Thus, people who have satisfying sexual relations have a higher quality of life and do not fail to express love and affection to their spouse, and have more understanding and empathy in life (16). As a result, if the sexual function is impaired, quality of life and marital satisfaction are affected.

Sexual dysfunction in women is demonstrated as sexual disorders including hypoactive sexual desire disorder (HSDD), which itself involves the absence of sexual fantasies, sexual arousal disorders, orgasmic disorders, sexual pain disorders (dyspareunia), general medical disorders, substance use disorders, and unclassified sexual disorders (17, 18). Although sexual desires are innate and involuntary, sexual attitudes and behaviors can be learned. Therefore, sexual activities can have different meanings for different people and change from time to time. Accordingly, by increasing awareness, the person acquires the necessary ability to solve sexual problems (19). This awareness is gained by increased education on sexual issues.

Education is a process that starts with informing, is followed by creating motivation, and ultimately leads to improved behavior and performance (20). Health literacy is one of the most important determinants of health in the world (21), practicing health-promoting behaviors is one of the best ways to stay healthy (22), and participation is a key value for health promotion (23). Health-promoting behaviors include activities that enable people to take control of their health (22).

### 2. Objectives

Since pregnancy care and screening programs are very important, especially in high-risk pregnancies, and as few interventional studies have addressed mental and sexual health in women with GDM, the present study aimed to examine the effect of a sexual health promotion training program on the sexual function of pregnant women with GDM referring to comprehensive health centers in Zahedan, Iran in 2020.

### 3. Methods

This quasi-experimental study was conducted using a pretest-posttest design with two groups. The participants were 80 pregnant women with GDM referring to comprehensive health centers in Zahedan to receive prenatal care in 2020. The inclusion criteria were women in the age range of 18 - 40 years, gestational age of 30 - 30 weeks, the absence of physical illnesses affecting sexual function or known mental disorders, normal pregnancy, no history of pre-GDM, diagnosis of GDM based on routine tests performed according to national guidelines, no use of medications affecting glucose metabolism, the absence of sex ban, and obtaining a score of 28 or less on the Female Sexual Function Index (FSFI). The exclusion criteria were the occurrence of fetal and maternal complications or any traumatic accident during the course of study and absence or non-participation in more than one training session.

The sample size in this study was estimated as 17 individuals per group using the mean and standard deviation for sexual function in a similar study (Moradi et al., 2016) with 95% confidence interval (CI), 95% statistical test power, and based on the following formula. Given that the participants were selected using multi-stage sampling, the estimated sample size was multiplied by two. Thus, the number of participants in each group was 34 individuals. To ensure the sample adequacy and due to the possible dropouts, the sample size for each group was estimated as 40 individuals (total sample size: 80 individuals). To this end, clinics and health care centers were selected using a multi-stage method, and then the participants in each center were selected in proportion to the assigned sample size using convenience sampling (24):

Z1 – α/2 = 26.59; $X-1$ = 3.56; S1 = 1.96

Z1 – β =22.48; $X-2$= 3.00; S2 = 1.64

The data in this study were collected using two instruments: (1) the demographic information questionnaire assessed parental age; (2) the number of pregnancies, type of previous deliveries, parental occupation, parental education, body mass index (BMI), and ethnicity. Besides, the FSFI was completed by the participants as a self-report instrument.

#### 3.1. Female Sexual Function Index (FSFI)

This index was developed by Rosen et al. (2000) to measure female sexual function. It contains 19 items that measure sexual function in six independent domains: (1) desire (2 items), (2) arousal (4 items), (3) lubrication (4 items), (4) orgasm (3 items), (5) satisfaction (3 items), and (6) pain (3 items). The respondents are asked to choose the best option that shows their sexual function during the last four weeks. The answers are scored on a five-point Likert scale ranging from 0 to 4 (0 = never, 1 = rarely, 2 = occasionally, 3 = frequently, or 4 = almost always). To normalize the domains, the scores of each domain are added together and then multiplied by the corresponding factor load shown in Table 1. After the domains are normalized, the minimum and maximum scores for each domain are 1 and 6, respectively. The minimum and maximum scores for the whole index are obtained, and the sum of the scores for the six domains are equal to 2 and 36, respectively. Higher scores indicate better sexual functions in each domain and overall (25). The reliability and validity of the FSFI in Iran were assessed and confirmed by Mohammadi et al. (2008). To determine the validity of the index, its content validity was assessed using the content index of the instrument. The reliability of the instrument was evaluated and confirmed by calculating the Cronbach’s alpha coefficient, and the corresponding value was 0.87 (26). The reliability of the instrument in the present study was checked by measuring its internal consistency for the whole index, and the Cronbach’s alpha was 0.72.

Table 1. Scoring the Index Items
Desire 21 - 50.61.26
Arousal 40 - 50.306
Lubrication40 - 50.306
Orgasm 30 - 50.406
Satisfaction 30 - 5 or 1 - 50.40.86
Pain30 - 50.406
Total 19--236

After obtaining an ethics code from the Ethics Committee of Zahedan University of Medical Sciences and obtaining permission from officials of the University and affiliated health centers, the participants were selected using multi-stage sampling. Since Zahedan has five districts, we selected two centers from each district by drawing lots. To this end, the city was first divided into five northern, southern, eastern, western, and central districts, and two health care centers were selected randomly from each district (10 centers in total). From the two selected centers in each district, one center was allocated to the intervention group and one center to the control group. Then, in each center, eight women who met the inclusion criteria were selected using convenience sampling. Next, a list of all pregnant women with GDM in each center was prepared using the data from the electronic systems of selected health centers, and they were contacted by phone. Necessary information was given to them about the objectives of the study. If they agreed to participate in the study, they were enrolled in the study after obtaining a written informed consent. Before the intervention, the participants in the intervention and control groups completed the two questionnaires. Moreover, the FSFI was administered again in both groups four weeks after the completion of the sexual health promotion training program.

Given the COVID-19 outbreak, the pregnant women in the intervention group were divided into small groups, each with 4 to 5 members. Then, they were invited to participate in the counseling sessions by telephone. The location of the training program was chosen upon the participants' agreement, and four sexual health promotion counseling training sessions (two 60- to 90-minute sessions per week) were held in the clinic or the School of Nursing and Midwifery in Zahedan by maintaining social distancing and observing health protocols such as wearing masks and gloves due to the coronavirus disease 2019 (COVID-19) pandemic. The instructions provided in the training sessions are presented in Table 2. To answer the possible questions and address the concerns of the participants in the intervention group after the intervention, a direct telephone line was provided to them. Four weeks after the completion of the intervention, the participants in both groups were asked to complete the FSFI. During this period, the participants in the control group received only routine training and care in the centers.

Table 2. The Instructional Content of the Training Program
Session The Instructional Content
1An overview of the anatomy and physiology of the male and female reproductive system and its changes during pregnancy in simple language and based on participants’ perceptions, psychological changes in different stages of pregnancy, sexual response cycle in men and women, changes in the sexual response cycle in pregnancy, common sexual misconceptions, and challenging them through group discussions.
2Exploring the attitudes towards sexual activity in pregnancy, a review of pregnancy-specific sexual disorders, the role of sex in marital relationships, and demonstrating effective and safe situations for sexual activity in pregnancy.
3Managing pregnancy stress by practicing and applying stress reduction techniques such as imaging and progressive muscle relaxation, listening to music, managing emotions and using problem-focused coping mechanisms, and training to manage anxiety-related thoughts through distraction and positive self-talk.
4Providing information on effective health care and lifestyles to cope with GMD by reviewing GMD and its complications, permitted physical activity training, proper diet training, self-care training, and psychological aspects of GMD, including worries and stress and their impact on women’s mental and sexual health.

The collected and coded data were analyzed using SPSS software (version 24). To this end, the data were summarized using descriptive statistics such as frequency (percentage), mean (± SD), minimum, and maximum. To compare the pre- and post-intervention mean scores in each group and between the groups, the paired samples t-test, and independent samples t-test were used, respectively. Moreover, to compare the frequency of the qualitative variables in the two groups, the Monte Carlo, Fisher, and chi-square tests were used. Analysis of covariance (ANCOVA) was also run to determine the effectiveness of the intervention and control the effect of the pretest. All statistical procedures were performed at the significance level of less than 0.05 (P < 0.05).

### 4. Results

Given the number of participants in each of the intervention and control groups, the data from 40 pregnant women with GDM were analyzed. As shown in Table 3, the participants and their husbands in the intervention and control groups were in their 20s and 30s, respectively. Moreover, the participants in both groups had married on average for more than seven years. The mean fasting blood sugar of the participants in both groups was within the normal controlled range. The results of the independent samples t-test showed that there was no significant difference between the two groups in terms of age and marriage length. Besides, the results of the chi-square and Mont Carlo tests showed no significant differences in terms of other qualitative variables (P < 0.05).

Table 3. A Comparison of the Demographic Characteristics of the Participants in the Two Groups a
VariablesGroupsP-Value
InterventionControl
Woman’s age 28.50 ± 6.0928.98 ± 5.030.77
Husband’s age 33.73 ± 5.7334.08 ± 4.980.77
Marriage length 7.58 ± 3.887.30 ± 2.910.72
BMI27.68 ± 1.9227.54 ± 2.190.86
Number of pregnancies 2.73 ± 1.122.85 ± 0.860.99
Fasting blood sugar 96.78 ± 11.68101.18 ± 14.730.07
Type of delivery0.11
Natural12 (0.30)12 (0.30)
C-section20 (0.50)26 (0.65)
Nulligravida8 (0.20) 82 (0.5)
History of abortion 0.64
No26 (0.65)24 (0.60)
Yes14 (0.35)16 (0.40)
Occupation 0.47
Unemployed25 (5.62)28 (0.70)
Employed15 (5.37)12 (0.30)
Education 0.98
Middle school12 (0.30)22 (0.55)
Secondary school23 (5.57)14 (0.35)
Higher education5 (5.12)4 (0.10)
Husband’s education 0.21
Illiterate2 (0.5)3 (5.7)
Middle school9 (5.22)15 (5.37)
Secondary school12 (0.30)5 (5.12)
Higher education17 (5.42)17 (5.42)
Type of pregnancy 0.39
Planned34 (0.85)31 (5.77)
Unplanned6 (0.15)9 (5.22)
Husband’s occupation 0.49
Unemployed0 (0.0) 02 (5)
Employed40 (100)38 (95)

a Values are expressed as mean ± SD or No. (%).

Table 4 shows the sexual function scores for the pregnant women with GDM in the intervention and control groups before the intervention (3.09 ± 0.86 and 2.86 ± 72, respectively) and after the intervention (3.75 ± 0.93 and 2.98 ± 0.55, respectively). The results of the independent samples t-test indicated no significant difference between the two groups in sexual function and its domains before the intervention (P > 0.05). However, significant differences were found between the two groups in sexual function and its domains after the intervention (P <0.05). The results of the paired samples t-test showed that the scores for sexual function and its domains (except for satisfaction and desire) significantly increased for the participants in the two groups after the intervention compared to the pre-intervention stage (P < 0.05). Given the significant differences in the mean scores of sexual function between the two groups before the intervention, the results of ANCOVA to control the significant effect of the pre-intervention scores showed that the mean scores of sexual function were significantly higher for the participants in the intervention group compared to the control group (P = 0.001) (Table 5).

Table 4. A Comparison of Sexual Function of the Participants in the Two Groups a
Variables StageChangesPaired Samples t-test
Pre-interventionPost-intervention
Desire
Intervention3.09 ± 0.863.75 ± 0.930.66 ± 0.670.001
Control2.86 ± 0.722.98 ± 0.550.12 ± 0.640.024
Independent samples t-testP = 0.21P = 0.001P = 0.001
Arousal
Intervention2.62 ± 0.973.24 ± 0.620.62 ± 0.430.001
Control2.16 ± 0.502.40 ± 0.620.24 ± 0.490.004
Independent samples t-testP = 0.009P = 0.001P = 0.001
Lubrication
Intervention3.09 ± 0.943.72 ± 0.620.36 ± 0.560.001
Control2.54 ± 0.732.71 ± 0.560.17 ± 0.470.02
Independent samples t-testP = 0.005P = 0.001P = 0.001
Orgasm
Intervention3.03 ± 0.824.04 ± 0.630.99 ± 0.600.001
Control2.67 ± 0.952.95 ± 0.660.28 ± 0.850.04
Independent samples t-testP = 0.07P = 0.001P = 0.001
Satisfaction
Intervention3.04 ± 0.854.21 ± 0.671.17 ± 0.540.001
Control2.78 ± 1.022.81 ± 0.790.03 ± 0.610.76
Independent samples t-testP =0.22P = 0.001P = 0.001
Pain
Intervention2.78 ± 0.823.94 ± 0.591.16 ± 0.630.001
Control2.61 ± 0.932.92 ± 0.750.13 ± 0.820.02
Independent samples t-testP = 0.39P = 0.001P = 0.001
Total score
Intervention17.65 ± 4.4122.89 ± 3.235.24 ± 2.230.001
Control15.62 ± 3.7916.78 ± 3.161.15 ± 3.130.02
Independent samples t-testP = 0.03P = 0.001P = 0.001

a Values are expressed as mean ± SD unless otherwise indicated.

Table 5. Results of ANCOVA to Compare the Post-Intervention Mean Scores of Sexual Function
Source Sum of SquaresdfMean SquareFSig.Effect SizePower
Pretest 450.421450.4299.290.0010.651
Group 457.921457.92100.940.0010.651
Error 349.29774.53
Total 33029.7080

### 5. Discussion

The data in this study showed that the sexual health promotion training program had a positive and significant effect on the overall sexual function of the pregnant women with GDM, so that sexual function and its domains were significantly improved after the intervention in the intervention group compared to the control group. To demonstrate the effectiveness of sexual health education on the promotion of sexual function, especially in pregnant women with diabetes, Mansouri et al. (2020) examined the effect of sexual health education based on the health belief model and Pender’s health promotion model on the sexual performance of women with type 2 diabetes and found that the use of both training models can significantly improve all aspects of sexual function in diabetic women, and there was no significant difference between the two groups. However, the health belief model was significantly more efficient than Pender’s health promotion model in terms of psychological stimulation (27). Nezamnia et al. (2020) examined the effectiveness of cognitive-behavioral therapy in sexual function in pregnant women, and showed that this treatment was effective in improving all domains of female sexual function two and four weeks after the psychological intervention (28). These findings are consistent with the results of the present study in terms of the impact of intervention techniques on all aspects of sexual function, while the training and intervention techniques in the two studies were slightly different.

Marvi et al. (2019) examined the effect of sexual health model training on the sexual function of women with infertility and showed that sexual health training had a significant effect on improving sexual function, including desire, lubrication, arousal, and orgasm in infertile women with serious psychological problems (29). Esposito et al. (2004) examined the effect of lifestyle change on sexual function in obese men with erectile dysfunction and found that using a healthy lifestyle improves sexual function in these men (30). Following the findings of the present study, these studies showed that psychological training of any kind can have positive and significant changes in improving the quality of sexual life of patients (31). Given that healthy lifestyle education can promote various aspects of mental health and sexual function in women of reproductive ages, sexual function can be improved with effective and standard training interventions (32).

The results of the present study showed that in addition to the group receiving sexual health promotion training, the participants in the control group who received no training intervention reported significant changes in their sexual function, especially in the domains of arousal, lubrication, orgasm, and pain. Perhaps factors such as receiving routine training and care during pregnancy from comprehensive health centers, possible visits to the doctor for GDM, and pregnancy progression changed the sexual function of the women in the control group.

Hashem et al. (2020) studied the effect of sexual health promotion training programs on the sexual function of pregnant women and found that implementing such training programs can significantly improve the sexual function of pregnant women. It was also shown that the sexual function of pregnant women was significantly different in each trimester (33). These findings provided empirical support for the results of the present study indicating the significant improvement in sexual function of pregnant women with increasing gestational age. However, Davari-Tanha et al. (2020) examined female sexual dysfunction in each trimester and showed that the difference in sexual function in the second trimester was less than in the first and third trimesters (34). Hajnasiri et al. also showed that increasing gestational age from the first trimester to the third trimester caused a gradual increase in sexual dysfunction in each trimester compared to the previous trimester (35). The results of these studies were not in line with the present study. Perhaps the reason for this discrepancy was that the intervention in the present study began during the first trimester of pregnancy.

According to the findings of previous studies and the present study, it can be concluded that education in women at risk of decreased sexual function, especially women with GDM, can enhance all domains of sexual function, and ultimately improve the quality of life in these women. However, despite the prohibition of discussing sexual issues in some cultures, including the Iranian community, various studies have shown that sex education is effective and sexual issues are influenced by any direct or indirect education.

Some of the limitations of this study included difficulty in talking about sexual issues and problems due to cultural norms of Iranian society, the impossibility of men’s participation in the training program, impossibility of forming larger training groups due to the COVID-19 outbreak, and not examining the retention effects of the training program in the postpartum period.

#### 5.1. Conclusion

The results of present study showed that the sexual health promotion training program promoted overall sexual function and its domains in pregnant women with GDM. Given the effectiveness of this training intervention, it is suggested that the sexual health promotion program developed in this study be integrated into pregnancy care programs for women with GDM to increase the health and well-being of this group of vulnerable women.

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• Copyright © 2021, Medical - Surgical Nursing Journal. This is an open-access article distributed under the terms of the Creative Commons Attribution-NonCommercial 4.0 International License (http://creativecommons.org/licenses/by-nc/4.0/) which permits copy and redistribute the material just in noncommercial usages, provided the original work is properly cited.


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 Control Theory from the Geometric Viewpoint  ¹«·á¹è¼Û

 ÁöÀºÀÌ : Andrei Agrachev, Yuri Sachkov ÃâÆÇ»ç : Springer-Verlag ÆÇ¼ö : 1 edition ÆäÀÌÁö¼ö : 412 pages ISBN : 3540210199
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 This book presents some facts and methods of Mathematical Control Theory treated from the geometric viewpoint. It is devoted to finite-dimensional deterministic control systems governed by smooth ordinary differential equations. The problems of controllability, state and feedback equivalence, and optimal control are studied. Some of the topics treated by the authors are covered in monographic or textbook literature for the first time while others are presented in a more general and flexible setting than elsewhere. Although being fundamentally written for mathematicians, the authors make an attempt to reach both the practitioner and the theoretician by blending the theory with applications. They maintain a good balance between the mathematical integrity of the text and the conceptual simplicity that might be required by engineers. It can be used as a text for graduate courses and will become most valuable as a reference work for graduate students and researchers. 1 Vector Fields and Control Systems on Smooth Manifolds 1 1.1 Smooth Manifolds 1 1.2 Vector Fields on Smooth Manifolds 4 1.3 Smooth Differential Equations and Flows on Manifolds 8 1.4 Control Systems 12 2 Elements of Chronological Calculus 21 2.1 Points, Diffeomorphisms, and Vector Fields 21 2.2 Seminorms and $C^{\infty }(M)$-Topology 25 2.3 Families of Functionals and Operators 26 2.4 Chronological Exponential 28 2.5 Action of Diffeomorphisms on Vector Fields 37 2.6 Commutation of Flows 40 2.7 Variations Formula 41 2.8 Derivative of Flow with Respect to Parameter 43 3 Linear Systems 47 3.1 Cauchy's Formula for Linear Systems 47 3.2 Controllability of Linear Systems 49 4 State Linearizability of Nonlinear Systems 53 4.1 Local Linearizability 53 4.2 Global Linearizability 57 5 The Orbit Theorem and its Applications 63 5.1 Formulation of the Orbit Theorem 63 5.2 Immersed Submanifolds 64 5.3 Corollaries of the Orbit Theorem 66 5.4 Proof of the Orbit Theorem 67 5.5 Analytic Case 72 5.6 Frobenius Theorem 74 5.7 State Equivalence of Control Systems 76 6 Rotations of the Rigid Body 81 6.1 State Space 81 6.2 Euler Equations 84 6.3 Phase Portrait 88 6.4 Controlled Rigid Body: Orbits 90 7 Control of Configurations 97 7.1 Model 97 7.2 Two Free Points 100 7.3 Three Free Points 101 7.4 Broken Line 104 8 Attainable Sets 109 8.1 Attainable Sets of Full-Rank Systems 109 8.2 Compatible Vector Fields and Relaxations 113 8.3 Poisson Stability 116 8.4 Controlled Rigid Body: Attainable Sets 118 9 Feedback and State Equivalence of Control Systems 121 9.1 Feedback Equivalence 121 9.2 Linear Systems 123 9.3 State-Feedback Linearizability 131 10 Optimal Control Problem 137 10.1 Problem Statement 137 10.2 Reduction to Study of Attainable Sets 138 10.3 Compactness of Attainable Sets 140 10.4 Time-Optimal Problem 143 10.5 Relaxations 143 11 Elements of Exterior Calculus and Symplectic Geometry 145 11.1 Differential 1-Forms 145 11.2 Differential $k$-Forms 147 11.3 Exterior Differential 151 11.4 Lie Derivative of Differential Forms 153 11.5 Elements of Symplectic Geometry 157 12 Pontryagin Maximum Principle 167 12.1 Geometric Statement of PMP and Discussion 167 12.2 Proof of PMP 172 12.3 Geometric Statement of PMP for Free Time 177 12.4 PMP for Optimal Control Problems 179 12.5 PMP with General Boundary Conditions 182 13 Examples of Optimal Control Problems 191 13.1 The Fastest Stop of a Train at a Station 191 13.2 Control of a Linear Oscillator 194 13.3 The Cheapest Stop of a Train 197 13.4 Control of a Linear Oscillator with Cost 199 13.5 Dubins Car 200 14 Hamiltonian Systems with Convex Hamiltonians 207 15 Linear Time-Optimal Problem 211 15.1 Problem Statement 211 15.2 Geometry of Polytopes 212 15.3 Bang-Bang Theorem 213 15.4 Uniqueness of Optimal Controls and Extremals 215 15.5 Switchings of Optimal Control 218 16 Linear-Quadratic Problem 223 16.1 Problem Statement 223 16.2 Existence of Optimal Control 224 16.3 Extremals 227 16.4 Conjugate Points 229 17 Sufficient Optimality Conditions, Hamilton-Jacobi Equation,Dynamic Programming 235 17.1 Sufficient Optimality Conditions 235 17.2 Hamilton-Jacobi Equation 242 17.3 Dynamic Programming 244 18 Hamiltonian Systems for Geometric Optimal Control Problems 247 18.1 Hamiltonian Systems on Trivialized Cotangent Bundle 247 18.2 Lie Groups 255 18.3 Hamiltonian Systems on Lie Groups 260 19 Examples of Optimal Control Problems on Compact Lie Groups 265 19.1 Riemannian Problem 265 19.2 A Sub-Riemannian Problem 267 19.3 Control of Quantum Systems 271 19.4 A Time-Optimal Problem on $SO(3)$ 284 20 Second Order Optimality Conditions 293 20.1 Hessian 293 20.2 Local Openness of Mappings 297 20.3 Differentiation of the Endpoint Mapping 304 20.4 Necessary Optimality Conditions 309 20.5 Applications 318 20.6 Single-Input Case 321 21 Jacobi Equation 333 21.1 Regular Case: Derivation of Jacobi Equation 334 21.2 Singular Case: Derivation of Jacobi Equation 338 21.3 Necessary Optimality Conditions 342 21.4 Regular Case: Transformation of Jacobi Equation 343 21.5 Sufficient Optimality Conditions 346 22 Reduction 355 22.1 Reduction 355 22.2 Rigid Body Control 358 22.3 Angular Velocity Control 359 23 Curvature 363 23.1 Curvature of 2-Dimensional Systems 363 23.2 Curvature of 3-Dimensional Control-Affine Systems 373 24 Rolling Bodies 377 24.1 Geometric Model 377 24.2 Two-Dimensional Riemannian Geometry 379 24.3 Admissible Velocities 383 24.4 Controllability 384 24.5 Length Minimization Problem 387 A Appendix 393 A.1 Homomorphisms and Operators in $C^{\infty }(M)$ 393 A.2 Remainder Term of the Chronological Exponential 395 References 399 List of Figures 407 Index 409 "This is a beautiful introduction to the subject.The authors gave a very personal touch to the subject, and have enriched the book with their well reputable wisdom in the subject.Wit comments abound everywhere (e.g. see preface, where controlled dynamical systems are compared to the assumption of free will), and instead a full blown over-generalized exposition they appeal instead to digestible but insightful bites of the theory.Since I'm not acquainted with the previous reviewer level of expertise in the subject, it's hard to figure out his personal reasons for an irate attack to the notation in the present book.If truth be said, this is a book for a well-educated gentleman or madam in the arts of mathematical sciences -- way beyond perhaps a more utilitarian introduction based on Matlab for example. This includes not only mathematicians, but physicists and control engineers too concerned about foundational aspect of their subject matter.Last but not least permit me to appraise briefly some examples contained herein.Agrachev et al.'s book is one of the few treatises dealing with rolling problems, a classic problem in nonholonomic control.Optimal control is also gracefully illustrated too. See for example a worked exercise on the fastest stop of a passenger train, or optimal control of a rigid body. (Engineers interested in attitude control may consider have a quick glance at a more mathematical formulation of the problem.)Not to appeal to academic authority, but both authors descend from Pontryagin's control school in Moscow. In fact the senior author Agrached is an academic grandson of Pontryagin himself, and therefore I'd like to view this book as a near first-account explanation of inner workings of the maximum principle.It is unfortunate that the previous reviewer had to in a harsh manner misjudge such superb book based only on notational strength."
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• ### Dark Energy Survey Year 1 Results: Cosmological Constraints from Galaxy Clustering and Weak Lensing(1708.01530)

March 1, 2019 astro-ph.CO
We present cosmological results from a combined analysis of galaxy clustering and weak gravitational lensing, using 1321 deg$^2$ of $griz$ imaging data from the first year of the Dark Energy Survey (DES Y1). We combine three two-point functions: (i) the cosmic shear correlation function of 26 million source galaxies in four redshift bins, (ii) the galaxy angular autocorrelation function of 650,000 luminous red galaxies in five redshift bins, and (iii) the galaxy-shear cross-correlation of luminous red galaxy positions and source galaxy shears. To demonstrate the robustness of these results, we use independent pairs of galaxy shape, photometric redshift estimation and validation, and likelihood analysis pipelines. To prevent confirmation bias, the bulk of the analysis was carried out while blind to the true results; we describe an extensive suite of systematics checks performed and passed during this blinded phase. The data are modeled in flat $\Lambda$CDM and $w$CDM cosmologies, marginalizing over 20 nuisance parameters, varying 6 (for $\Lambda$CDM) or 7 (for $w$CDM) cosmological parameters including the neutrino mass density and including the 457 $\times$ 457 element analytic covariance matrix. We find consistent cosmological results from these three two-point functions, and from their combination obtain $S_8 \equiv \sigma_8 (\Omega_m/0.3)^{0.5} = 0.783^{+0.021}_{-0.025}$ and $\Omega_m = 0.264^{+0.032}_{-0.019}$ for $\Lambda$CDM for $w$CDM, we find $S_8 = 0.794^{+0.029}_{-0.027}$, $\Omega_m = 0.279^{+0.043}_{-0.022}$, and $w=-0.80^{+0.20}_{-0.22}$ at 68% CL. The precision of these DES Y1 results rivals that from the Planck cosmic microwave background measurements, allowing a comparison of structure in the very early and late Universe on equal terms. Although the DES Y1 best-fit values for $S_8$ and $\Omega_m$ are lower than the central values from Planck ...
• ### Dark Energy Survey Year 1 Results: Cosmological Constraints from Cosmic Shear(1708.01538)

April 30, 2018 astro-ph.CO
We use 26 million galaxies from the Dark Energy Survey (DES) Year 1 shape catalogs over 1321 deg$^2$ of the sky to produce the most significant measurement of cosmic shear in a galaxy survey to date. We constrain cosmological parameters in both the flat $\Lambda$CDM and $w$CDM models, while also varying the neutrino mass density. These results are shown to be robust using two independent shape catalogs, two independent \photoz\ calibration methods, and two independent analysis pipelines in a blind analysis. We find a 3.5\% fractional uncertainty on $\sigma_8(\Omega_m/0.3)^{0.5} = 0.782^{+0.027}_{-0.027}$ at 68\% CL, which is a factor of 2.5 improvement over the fractional constraining power of our DES Science Verification results. In $w$CDM, we find a 4.8\% fractional uncertainty on $\sigma_8(\Omega_m/0.3)^{0.5} = 0.777^{+0.036}_{-0.038}$ and a dark energy equation-of-state $w=-0.95^{+0.33}_{-0.39}$. We find results that are consistent with previous cosmic shear constraints in $\sigma_8$ -- $\Omega_m$, and see no evidence for disagreement of our weak lensing data with data from the CMB. Finally, we find no evidence preferring a $w$CDM model allowing $w\ne -1$. We expect further significant improvements with subsequent years of DES data, which will more than triple the sky coverage of our shape catalogs and double the effective integrated exposure time per galaxy.
• ### Measurement of camera image sensor depletion thickness with cosmic rays(1511.00660)

Camera image sensors can be used to detect ionizing radiation in addition to optical photons. In particular, cosmic-ray muons are detected as long, straight tracks passing through multiple pixels. The distribution of track lengths can be related to the thickness of the active (depleted) region of the camera image sensor through the known angular distribution of muons at sea level. We use a sample of cosmic-ray muon tracks recorded by the Distributed Electronic Cosmic-ray Observatory to measure the thickness of the depletion region of the camera image sensor in a commercial smart phone, the HTC Wildfire S. The track length distribution prefers a cosmic-ray muon angular distribution over an isotropic distribution. Allowing either distribution, we measure the depletion thickness to be between 13.9~$\mu$m and 27.7~$\mu$m. The same method can be applied to additional models of image sensor. Once measured, the thickness can be used to convert track length to incident polar angle on a per-event basis. Combined with a determination of the incident azimuthal angle directly from the track orientation in the sensor plane, this enables direction reconstruction of individual cosmic-ray events.
• ### Galaxy And Mass Assembly (GAMA): autoz spectral redshift measurements, confidence and errors(1404.2626)

The Galaxy And Mass Assembly (GAMA) survey has obtained spectra of over 230000 targets using the Anglo-Australian Telescope. To homogenise the redshift measurements and improve the reliability, a fully automatic redshift code was developed (autoz). The measurements were made using a cross-correlation method for both absorption-line and emission-line spectra. Large deviations in the high-pass filtered spectra are partially clipped in order to be robust against uncorrected artefacts and to reduce the weight given to single-line matches. A single figure of merit (FOM) was developed that puts all template matches onto a similar confidence scale. The redshift confidence as a function of the FOM was fitted with a tanh function using a maximum likelihood method applied to repeat observations of targets. The method could be adapted to provide robust automatic redshifts for other large galaxy redshift surveys. For the GAMA survey, there was a substantial improvement in the reliability of assigned redshifts and in the lowering of redshift uncertainties with a median velocity uncertainty of 33 km/s.
• ### Galaxy And Mass Assembly (GAMA): Testing galaxy formation models through the most massive galaxies in the Universe(1402.4139)

Feb. 17, 2014 astro-ph.CO
We have analysed the growth of Brightest Group Galaxies and Brightest Cluster Galaxies (BGGs/BCGs) over the last 3 billion years using a large sample of 883 galaxies from the Galaxy And Mass Assembly Survey. By comparing the stellar mass of BGGs and BCGs in groups and clusters of similar dynamical masses, we find no significant growth between redshift $z=0.27$ and $z=0.09$. We also examine the number of BGGs/BCGs that have line emission, finding that approximately 65 per cent of BGGs/BCGs show H$\alpha$ in emission. From the galaxies where the necessary spectroscopic lines were accurately recovered (54 per cent of the sample), we find that half of this (i.e. 27 per cent of the sample) harbour on-going star formation with rates up to $10\,$M$_{\odot}$yr$^{-1}$, and the other half (i.e. 27 per cent of the sample) have an active nucleus (AGN) at the centre. BGGs are more likely to have ongoing star formation, while BCGs show a higher fraction of AGN activity. By examining the position of the BGGs/BCGs with respect to their host dark matter halo we find that around 13 per cent of them do not lie at the centre of the dark matter halo. This could be an indicator of recent cluster-cluster mergers. We conclude that BGGs and BCGs acquired their stellar mass rapidly at higher redshifts as predicted by semi-analytic models, mildly slowing down at low redshifts.
• ### Spectroscopic Needs for Imaging Dark Energy Experiments: Photometric Redshift Training and Calibration(1309.5384)

Sept. 20, 2013 astro-ph.CO
Large sets of objects with spectroscopic redshift measurements will be needed for imaging dark energy experiments to achieve their full potential, serving two goals:_training_, i.e., the use of objects with known redshift to develop and optimize photometric redshift algorithms; and_calibration_, i.e., the characterization of moments of redshift (or photo-z error) distributions. Better training makes cosmological constraints from a given experiment stronger, while highly-accurate calibration is needed for photo-z systematics not to dominate errors. In this white paper, we investigate the required scope of spectroscopic datasets which can serve both these purposes for ongoing and next-generation dark energy experiments, as well as the time required to obtain such data with instruments available in the next decade. Large time allocations on kilo-object spectrographs will be necessary, ideally augmented by infrared spectroscopy from space. Alternatively, precision calibrations could be obtained by measuring cross-correlation statistics using samples of bright objects from a large baryon acoustic oscillation experiment such as DESI. We also summarize the additional work on photometric redshift methods needed to prepare for ongoing and future dark energy experiments.
• ### MOONS: a Multi-Object Optical and Near-infrared Spectrograph for the VLT(1208.5780)

MOONS is a new conceptual design for a Multi-Object Optical and Near-infrared Spectrograph for the Very Large Telescope (VLT), selected by ESO for a Phase A study. The baseline design consists of 1000 fibers deployable over a field of view of 500 square arcmin, the largest patrol field offered by the Nasmyth focus at the VLT. The total wavelength coverage is 0.8um-1.8um and two resolution modes: medium resolution and high resolution. In the medium resolution mode (R=4,000-6,000) the entire wavelength range 0.8um-1.8um is observed simultaneously, while the high resolution mode covers simultaneously three selected spectral regions: one around the CaII triplet (at R=8,000) to measure radial velocities, and two regions at R=20,000 one in the J-band and one in the H-band, for detailed measurements of chemical abundances. The grasp of the 8.2m Very Large Telescope (VLT) combined with the large multiplex and wavelength coverage of MOONS - extending into the near-IR - will provide the observational power necessary to study galaxy formation and evolution over the entire history of the Universe, from our Milky Way, through the redshift desert and up to the epoch of re-ionization at z>8-9. At the same time, the high spectral resolution mode will allow astronomers to study chemical abundances of stars in our Galaxy, in particular in the highly obscured regions of the Bulge, and provide the necessary follow-up of the Gaia mission. Such characteristics and versatility make MOONS the long-awaited workhorse near-IR MOS for the VLT, which will perfectly complement optical spectroscopy performed by FLAMES and VIMOS.
• Euclid is a space-based survey mission from the European Space Agency designed to understand the origin of the Universe's accelerating expansion. It will use cosmological probes to investigate the nature of dark energy, dark matter and gravity by tracking their observational signatures on the geometry of the universe and on the cosmic history of structure formation. The mission is optimised for two independent primary cosmological probes: Weak gravitational Lensing (WL) and Baryonic Acoustic Oscillations (BAO). The Euclid payload consists of a 1.2 m Korsch telescope designed to provide a large field of view. It carries two instruments with a common field-of-view of ~0.54 deg2: the visual imager (VIS) and the near infrared instrument (NISP) which contains a slitless spectrometer and a three bands photometer. The Euclid wide survey will cover 15,000 deg2 of the extragalactic sky and is complemented by two 20 deg2 deep fields. For WL, Euclid measures the shapes of 30-40 resolved galaxies per arcmin2 in one broad visible R+I+Z band (550-920 nm). The photometric redshifts for these galaxies reach a precision of dz/(1+z) < 0.05. They are derived from three additional Euclid NIR bands (Y, J, H in the range 0.92-2.0 micron), complemented by ground based photometry in visible bands derived from public data or through engaged collaborations. The BAO are determined from a spectroscopic survey with a redshift accuracy dz/(1+z) =0.001. The slitless spectrometer, with spectral resolution ~250, predominantly detects Ha emission line galaxies. Euclid is a Medium Class mission of the ESA Cosmic Vision 2015-2025 programme, with a foreseen launch date in 2019. This report (also known as the Euclid Red Book) describes the outcome of the Phase A study.
• BigBOSS is a Stage IV ground-based dark energy experiment to study baryon acoustic oscillations (BAO) and the growth of structure with a wide-area galaxy and quasar redshift survey over 14,000 square degrees. It has been conditionally accepted by NOAO in response to a call for major new instrumentation and a high-impact science program for the 4-m Mayall telescope at Kitt Peak. The BigBOSS instrument is a robotically-actuated, fiber-fed spectrograph capable of taking 5000 simultaneous spectra over a wavelength range from 340 nm to 1060 nm, with a resolution R = 3000-4800. Using data from imaging surveys that are already underway, spectroscopic targets are selected that trace the underlying dark matter distribution. In particular, targets include luminous red galaxies (LRGs) up to z = 1.0, extending the BOSS LRG survey in both redshift and survey area. To probe the universe out to even higher redshift, BigBOSS will target bright [OII] emission line galaxies (ELGs) up to z = 1.7. In total, 20 million galaxy redshifts are obtained to measure the BAO feature, trace the matter power spectrum at smaller scales, and detect redshift space distortions. BigBOSS will provide additional constraints on early dark energy and on the curvature of the universe by measuring the Ly-alpha forest in the spectra of over 600,000 2.2 < z < 3.5 quasars. BigBOSS galaxy BAO measurements combined with an analysis of the broadband power, including the Ly-alpha forest in BigBOSS quasar spectra, achieves a FOM of 395 with Planck plus Stage III priors. This FOM is based on conservative assumptions for the analysis of broad band power (kmax = 0.15), and could grow to over 600 if current work allows us to push the analysis to higher wave numbers (kmax = 0.3). BigBOSS will also place constraints on theories of modified gravity and inflation, and will measure the sum of neutrino masses to 0.024 eV accuracy.
• ### GAMA/H-ATLAS: The ultraviolet spectral slope and obscuration in galaxies(1103.3080)

March 27, 2011 astro-ph.CO
We use multiwavelength data from the Galaxy And Mass Assembly (GAMA) and Herschel ATLAS (H-ATLAS) surveys to compare the relationship between various dust obscuration measures in galaxies. We explore the connections between the ultraviolet (UV) spectral slope, $\beta$, the Balmer decrement, and the far infrared (IR) to $150\,$nm far ultraviolet (FUV) luminosity ratio. We explore trends with galaxy mass, star formation rate (SFR) and redshift in order to identify possible systematics in these various measures. We reiterate the finding of other authors that there is a large scatter between the Balmer decrement and the $\beta$ parameter, and that $\beta$ may be poorly constrained when derived from only two broad passbands in the UV. We also emphasise that FUV derived SFRs, corrected for dust obscuration using $\beta$, will be overestimated unless a modified relation between $\beta$ and the attenuation factor is used. Even in the optimum case, the resulting SFRs have a significant scatter, well over an order of magnitude. While there is a stronger correlation between the IR to FUV luminosity ratio and $\beta$ parameter than with the Balmer decrement, neither of these correlations are particularly tight, and dust corrections based on $\beta$ for high redshift galaxy SFRs must be treated with caution. We conclude with a description of the extent to which the different obscuration measures are consistent with each other as well as the effects of including other galactic properties on these correlations.
• ### Galaxy and Mass Assembly (GAMA): Dust obscuration in galaxies and their recent star formation histories(1009.0616)

Sept. 3, 2010 astro-ph.CO
We present self-consistent star formation rates derived through pan-spectral analysis of galaxies drawn from the Galaxy and Mass Assembly (GAMA) survey. We determine the most appropriate form of dust obscuration correction via application of a range of extinction laws drawn from the literature as applied to Halpha, [O{II}] and UV luminosities. These corrections are applied to a sample of 31,508 galaxies from the GAMA survey at z < 0.35. We consider several different obscuration curves, including those of Milky Way, Calzetti (2001) and Fischera and Dopita (2005) curves and their effects on the observed luminosities. At the core of this technique is the observed Balmer decrement, and we provide a prescription to apply optimal obscuration corrections using the Balmer decrement. We carry out an analysis of the star formation history (SFH) using stellar population synthesis tools to investigate the evolutionary history of our sample of galaxies as well as to understand the effects of variation in the Initial Mass Function (IMF) and the effects this has on the evolutionary history of galaxies. We find that the Fischera and Dopita (2005) obscuration curve with an R_{v} value of 4.5 gives the best agreement between the different SFR indicators. The 2200A feature needed to be removed from this curve to obtain complete consistency between all SFR indicators suggesting that this feature may not be common in the average integrated attenuation of galaxy emission. We also find that the UV dust obscuration is strongly dependent on the SFR.
• ### The Herschel ATLAS(0910.4279)

Oct. 22, 2009 astro-ph.CO
The Herschel ATLAS is the largest open-time key project that will be carried out on the Herschel Space Observatory. It will survey 510 square degrees of the extragalactic sky, four times larger than all the other Herschel surveys combined, in five far-infrared and submillimetre bands. We describe the survey, the complementary multi-wavelength datasets that will be combined with the Herschel data, and the six major science programmes we are undertaking. Using new models based on a previous submillimetre survey of galaxies, we present predictions of the properties of the ATLAS sources in other wavebands.
• ### The SCUBA Half Degree Extragalactic Survey (SHADES) - IX: the environment, mass and redshift dependence of star formation(0712.3613)

March 5, 2008 astro-ph
We present a comparison between the SCUBA Half Degree Extragalactic Survey (SHADES) at 450 and 850 microns in the Lockman Hole East with a deep Spitzer Space Telescope survey at 3.6-24 microns conducted in Guaranteed Time. Using stacking analyses we demonstrate a striking correspondence between the galaxies contributing the submm extragalactic background light, with those likely to dominate the backgrounds at Spitzer wavelengths. Using a combination BRIzK plus Spitzer photometric redshifts, we show that at least a third of the Spitzer-identified submm galaxies at 1<z<1.5 appear to reside in overdensities when the density field is smoothed at 0.5-2 Mpc comoving diameters, supporting the high-redshift reversal of the local star formation - galaxy density relation. We derive the dust-shrouded cosmic star formation history of galaxies as a function of assembled stellar masses. For model stellar masses <10^11 Msun, this peaks at lower redshifts than the ostensible z~2.2 maximum for submm point sources, adding to the growing consensus for downsizing'' in star formation. Our surveys are also consistent with downsizing'' in mass assembly. Both the mean star formation rates <dM/dt> and specific star formation rates <(1/M)dM/dt> are in striking disagreement with some semi-analytic predictions from the Millenium simulation. The discrepancy could either be resolved with a top-heavy initial mass function, or a significant component of the submm flux heated by the interstellar radiation field.
• ### The 2dF Galaxy Redshift Survey: correlation functions, peculiar velocities and the matter density of the Universe(astro-ph/0212375)

Aug. 5, 2003 astro-ph
We present a detailed analysis of the two-point correlation function, from the 2dF Galaxy Redshift Survey (2dFGRS). We estimate the redshift-space correlation function, xi(s), from which we measure the redshift-space clustering length, s_0=6.82+/-0.28 Mpc/h. We also estimate the projected correlation function, Xi(sigma), and the real-space correlation function, xi(r), which can be fit by a power-law, with r_0=5.05+/-0.26Mpc/h, gamma_r=1.67+/-0.03. For r>20Mpc/h, xi drops below a power-law as is expected in the popular LCDM model. The ratio of amplitudes of the real and redshift-space correlation functions on scales of 8-30Mpc/h gives an estimate of the redshift-space distortion parameter beta. The quadrupole moment of xi on scales 30-40Mpc/h provides another estimate of beta. We also estimate the distribution function of pairwise peculiar velocities, f(v), including rigorously the effect of infall velocities, and find that it is well fit by an exponential. The accuracy of our xi measurement is sufficient to constrain a model, which simultaneously fits the shape and amplitude of xi(r) and the two redshift-space distortion effects parameterized by beta and velocity dispersion, a. We find beta=0.49+/-0.09 and a=506+/-52km/s, though the best fit values are strongly correlated. We measure the variation of the peculiar velocity dispersion with projected separation, a(sigma), and find that the shape is consistent with models and simulations. Using the constraints on bias from recent estimates, and taking account of redshift evolution, we conclude that beta(L=L*,z=0)=0.47+/-0.08, and that the present day matter density of the Universe is 0.3, consistent with other 2dFGRS estimates and independent analyses.
• ### The 2dF Galaxy Redshift Survey: galaxy clustering per spectral type(astro-ph/0303668)

March 31, 2003 astro-ph
We have calculated the two-point correlation functions in redshift space, xi(sigma,pi), for galaxies of different spectral types in the 2dF Galaxy Redshift Survey. Using these correlation functions we are able to estimate values of the linear redshift-space distortion parameter, beta = Omega_m^0.6/b, the pairwise velocity dispersion, a, and the real-space correlation function, xi(r), for galaxies with both relatively low star-formation rates (for which the present rate of star formation is less than 10% of its past averaged value) and galaxies with higher current star-formation activity. At small separations, the real-space clustering of passive galaxies is very much stronger than that of the more actively star-forming galaxies; the correlation-function slopes are respectively 1.93 and 1.50, and the relative bias between the two classes is a declining function of radius. On scales larger than 10 h^-1 Mpc there is evidence that the relative bias tends to a constant, b(passive)/b(active) ~ 1. This result is consistent with the similar degrees of redshift-space distortions seen in the correlation functions of the two classes -- the contours of xi(sigma,pi) require beta(active)=0.49+/-0.13, and beta(passive)=0.48+/-0.14. The pairwise velocity dispersion is highly correlated with beta. However, despite this a significant difference is seen between the two classes. Over the range 8-20 h^-1 Mpc, the pairwise velocity dispersion has mean values 416+/-76 km/s and 612+/-92 km/s for the active and passive galaxy samples respectively. This is consistent with the expectation from morphological segregation, in which passively evolving galaxies preferentially inhabit the cores of high-mass virialised regions.
• ### The 2dF Galaxy Redshift Survey: the luminosity function of cluster galaxies(astro-ph/0212562)

Dec. 30, 2002 astro-ph
We have determined the composite luminosity function (LF) for galaxies in 60 clusters from the 2dF Galaxy Redshift Survey. The LF spans the range $-22.5<M_{b_{\rm J}}<-15$, and is well-fitted by a Schechter function with ${M_{b_{\rm J}}}^{*}=-20.07\pm0.07$ and $\alpha=-1.28\pm0.03$ ($H_0$=100 km s$^{-1}$ Mpc$^{-1}$, $\Omega_M$=0.3, $\Omega_\Lambda$=0.7). It differs significantly from the field LF of \cite{mad02}, having a characteristic magnitude that is approximately 0.3 mag brighter and a faint-end slope that is approximately 0.1 steeper. There is no evidence for variations in the LF across a wide range of cluster properties. However the LF of early-type galaxies in clusters is both brighter and steeper than its field counterpart. The differences between the field and cluster LFs for the various spectral types can be qualitatively explained by the suppression of star formation in the dense cluster environment, together with mergers to produce the brightest early-type galaxies.
• ### The SCUBA 8-mJy survey - I: Sub-millimetre maps, sources and number counts(astro-ph/0107446)

Oct. 21, 2002 astro-ph
We present maps, source lists, and number counts from the largest, unbiassed, extragalactic sub-mm survey so far undertaken with the SCUBA camera on the JCMT. Our maps cover 260 sq. arcmin, to a noise level S(850)=2.5 mJy/beam. We have reduced the data using both SURF, and our own pipeline which produces zero-footprint maps and noise images. The uncorrelated noise maps produced by the latter approach have allowed application of a maximum-likelihood method to measure the statistical significance of each peak, leading to properly quantified flux-density errors for all potential sources. We detect 19 sources with S/N > 4, 38 with S/N > 3.5, and 72 with S/N > 3. To assess completeness and the impact of source confusion we have applied our source extraction algorithm to a series of simulated images. The result is a new estimate of the sub-mm source counts in the flux-density range S(850)=5-15mJy, which we compare with other estimates, and with model predictions. Our estimate of the cumulative source count at S(850) > 8 mJy is 320 (+80,-100) per square degree. Assuming that the majority of sources have z > 1.5, the co-moving number density of high-z galaxies forming stars at a rate >1000 solar masses per year is 10^-5 per Mpc^3, with only a weak dependence on the precise redshift distribution. This number density corresponds to that of massive ellipticals with L > 3-4 L* at low redshift and is also the same as the co-moving number density of comparably massive, passively-evolving objects in the redshift band 1<z<2 inferred from recent surveys of extremely red objects. Thus the bright sub-mm sources can plausibly account for the formation of all present-day massive ellipticals. Improved z constraints, and a proper measurement of sub-mm clustering can refine or refute this picture.
• ### The 2dF Galaxy Redshift Survey: The b_J-band galaxy luminosity function and survey selection function(astro-ph/0111011)

April 26, 2002 astro-ph
We use more than 110500 galaxies from the 2dF galaxy redshift survey (2dFGRS) to estimate the b_J-band galaxy luminosity function at redshift z=0, taking account of evolution, the distribution of magnitude measurement errors and small corrections for incompletenessin the galaxy catalogue. Throughout the interval -16.5>M- 5log h>-22, the luminosity function is accurately described by a Schechter function with M* -5log h =-19.66+/-0.07, alpha=-1.21+/-0.03 and phistar=(1.61+/-0.08) 10^{-2} h^3/Mpc^3, giving an integrated luminosity density of rho_L=(1.82+/-0.17) 10^8 h L_sol/Mpc^3 (assuming an Omega_0=0.3, Lambda_0=0.7 cosmology). The quoted errors have contributions from the accuracy of the photometric zeropoint, large scale structure in the galaxy distribution and, importantly, from the uncertainty in the appropriate evolutionary corrections. Our luminosity function is in excellent agreement with, but has much smaller statistical errors than an estimate from the Sloan Digital Sky Survey (SDSS) data when the SDSS data are accurately translated to the b_J-band and the luminosity functions are normalized in the same way. We use the luminosity function, along with maps describing the redshift completeness of the current 2dFGRS catalogue, and its weak dependence on apparent magnitude, to define a complete description of the 2dFGRS selection function. Details and tests of the calibration of the 2dFGRS photometric parent catalogue are also presented.
• ### Proposed identification of Hubble Deep Field submillimeter source HDF 850.1(astro-ph/9907139)

July 12, 1999 astro-ph
The IRAM interferometer has been used to detect the submm source HDF 850.1 found by Hughes et al. (1998) in the Hubble Deep Field. The flux density measured at 1.3mm is 2.2 mJy, in agreement with the flux density measured at the JCMT. The flux densities and upper limits measured at 3.4, 2.8, 1.3, 0.85, and 0.45 mm show that the emission is from dust. We suggest that the 1.3mm dust source is associated with the optical arc-like feature, 3-593.0, that has a photometric redshift of about 1.7. If HDF 850.1 is at this redshift and unlensed, its spectral energy distribution, combined with that of 3-593.0, matches closely that of the ultraluminous galaxy VII Zw 31. Another possibility is that the dust source may be gravitationally lensed by the elliptical galaxy 3-586.0 at a redshift of 1.